Search results “Matrix analysis and applied linear algebra meyer”

Seguimos com o problema de encontrar a Forma Escada e a Forma Escada Reduzida de uma matriz. Neste video incluiremos o ponto de vista das colunas da matriz.
Referência:
Carl D. Meyer. Matrix Analysis and Applied Linear Algebra.

Views: 113
Sergio Silva

Course 3 Mathematics for Machine Learning PCA: Module 4 Principal Component Analysis
To get certificate subscribe at: https://www.coursera.org/learn/pca-machine-learning
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Mathematics for Machine Learning: Multivariate Calculus https://www.youtube.com/playlist?list=PL2jykFOD1AWa-I7JQfdD-ScBB6XojzmVh
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Youtube channel: https://www.youtube.com/user/intrigano
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https://scsa.ge/en/online-courses/
https://www.facebook.com/cyberassociation/
About this course: This course introduces the mathematical foundations to derive Principal Component Analysis (PCA), a fundamental dimensionality reduction technique. We'll cover some basic statistics of data sets, such as mean values and variances, we'll compute distances and angles between vectors using inner products and derive orthogonal projections of data onto lower-dimensional subspaces. Using all these tools, we'll then derive PCA as a method that minimizes the average squared reconstruction error between data points and their reconstruction. At the end of this course, you'll be familiar with important mathematical concepts and you can implement PCA all by yourself. If you’re struggling, you'll find a set of jupyter notebooks that will allow you to explore properties of the techniques and walk you through what you need to do to get on track. If you are already an expert, this course may refresh some of your knowledge. This examples and exercises require: 1. Some ability of abstract thinking 2. Good background in linear algebra (e.g., matrix and vector algebra, linear independence, basis) 3. Basic background in multivariate calculus (e.g., partial derivatives, basic optimization) 4. Basic knowledge in python programming and numpy
Who is this class for: This is an intermediate level course. It is probably good to brush up your linear algebra and python programming before you start this course.
________________________________________
Created by: Imperial College London
Module 4 Principal Component Analysis
We can think of dimensionality reduction as a way of compressing data with some loss, similar to jpg or mp3. Principal Component Analysis (PCA) is one of the most fundamental dimensionality reduction techniques that are used in machine learning. In this module, we use the results from the first three modules of this course and derive PCA from a geometric point of view. Within this course, this module is the most challenging one, and we will go through an explicit derivation of PCA plus some coding exercises that will make us a proficient user of PCA.
Learning Objectives
• Summarize PCA
• Write code that implements PCA
• Assess the properties of PCA when applying to high-dimensional data

Views: 194
intrigano

Green Family Lecture Series 2018
“God May or May Not Play Dice but She Sure Loves a von Neumann Algebra”
Vaughan Jones, Vanderbilt University
Abstract: After reviewing the basic mathematics of quantum mechanics I will explain what a von Neumann algebra is and why it is as natural and necessary for understanding the quantum world as manifolds are for the classical world. An attempt to base quantum field theory on von Neumann algebras has, in the last 30 years, been extraordinarily successful in low dimensions. I will discuss a few of the high points of this theory.
Institute for Pure and Applied Mathematics, UCLA
May 2, 2018
For more information: http://www.ipam.ucla.edu/programs/public-lectures-events/green-family-lecture-series-god-may-or-may-not-play-dice-but-he-sure-loves-a-von-neumann-algebra-by-vaughan-jones/?tab=lecture-info

Views: 2210
Institute for Pure & Applied Mathematics (IPAM)

Many fields of mathematics are hundreds, or even thousands, of years old. By contrast, the Katsura Group researches operator algebra theory, which is a relatively new field, arising in 1929. It was originated by von Neumann, one of the 20th Century's most influential scientists, to describe quantum mechanics mathematically.
Q"Operating, in ordinary language, means acting on something. In my specialty, operator algebra, what's acted on is an abstract mathematical object called a Hilbert space. The subject that acts on the Hilbert space is called an operator. With operators, if you do one operation, then a different operation, and think of the two as a combined operation, a multiplicative structure arises. Also, the object called a Hilbert space involves an additive structure, and you can use that to define addition between operators. In mathematics, structures where addition and multiplication are conceivable are called algebras. In operator algebra theory, we investigate the various structures of algebras formed by operators."
The mathematical features of operator algebra theory can be expressed in three words: infinite, topology, and non-commutativity. Infinite means the object has an infinite size, and this results in various mysterious phenomena that don't arise in the finite world.
Also, in operator algebra theory, we don't exclude the infinite nature of objects as being pathological; instead, we try to tame it using various tools and methods. The most powerful tool is our second keyword, topology. In operator algebra theory, we try to control infinity using topology, which varies depending on situations. Different topologies lead different concepts, C*-algebras and von Neumann algebras.
Our last keyword, non-commutativity, expresses the phenomenon where considering a product in a different order changes the result. In ordinary arithmetic, products don't depend on order. But for operators, products may well depend on order, like matrix multiplication.
Q"I also do research on the borderline between set theory and operator algebra theory. Set theory involves research on infinite subjects, or infinity itself, more directly than operator algebra theory. One famous example is called the Hilbert Hotel."
The Hilbert Hotel has an infinite number of rooms. Even if it's full when a new customer arrives, the hotel can move the person staying in the Room 1 to Room 2, the person staying in Room 2 to Room 3, and so on, to make Room 1 vacant. Using this method, even if an infinite number of new customers arrive, the hotel can move the guest in Room 1 to Room 2, the guest in Room 2 to Room 4, the guest in Room 3 to Room 6, the guest in Room 4 to Room 8, and the guest in Room N to Room 2N, making all odd-numbered rooms vacant, so an infinite number of people can stay. Moreover, another phenomenon occurs: Even if an infinite number of buses each containing an infinite number of customers arrives, the hotel can arrange things so that all of the new customers can stay.
Research students in the Katsura Group also study the relationship between tiling and C* algebra, and tackle many topics in set theory and logic. In this way, the Group works to open up new frontiers in mathematics.
Q"I think that, in a great many cases, interesting topics lie on the borderline between related fields. Of course, it's important that students do specialized studies. But I'd also like our students to take an interest in other aspects of mathematics, along with techniques from various disciplines. Those could include physics, chemistry, and engineering, but also many other fields."

Views: 3884
慶應義塾Keio University

Applied Multivariate Statistical Modeling by Dr J Maiti,Department of Management, IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in

Views: 7926
nptelhrd

In mathematics, a matrix norm is a natural extension of the notion of a vector norm to matrices.
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Views: 4259
Audiopedia

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P2 = P. That is, whenever P is applied twice to any value, it gives the same result as if it were applied once. It leaves its image unchanged. Though abstract, this definition of "projection" formalizes and generalizes the idea of graphical projection. One can also consider the effect of a projection on a geometrical object by examining the effect of the projection on points in the object.
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Views: 382
Audiopedia

Google Tech Talk
March 27, 2012
ABSTRACT
It is often said that genomics science is on a Moore's law, growing exponentially in data throughput, number of assembled genomes, lowered cost, etc.; and yet, it has not delivered the biomedical promises made a decade ago: personalized medicine; genomic characterization of diseases like cancer, schizophrenia, and autism; bio-markers for common complex diseases; prenatal genomic assays, etc. What share of blame for this failure ought to be allocated to computer science (or computational biology, bioinformatics, statistical genetics, etc.)? How can the computational biology community lead genomics science to rescue it from the current impasse? What are the computational solutions to these problems? What should be our vision of computational biology in the coming decade? We will discuss three systems: TotalReCaller, SUTTA-Assembler and Feature-Response-Curves, in this context.
For more info: http://www.meetup.com/google-nyc-tech-talks/events/56229442/
About the speaker
Professor Bud Mishra is a professor of computer science and mathematics at NYU's Courant Institute of Mathematical Sciences, professor of human genetics at Mt. Sinai School of Medicine, and a professor of cell biology at NYU School of Medicine. He founded the NYU/Courant Bioinformatics Group, a multi-disciplinary group working on research at the interface of computer science, applied mathematics, biology, biomedicine and bio/nano-technologies. Prof. Mishra has a degree in Physics from Utkal University, in Electronics and Communication Engineering from IIT, Kharagpur, and MS and PhD degrees in Computer Science from Carnegie-Mellon University. He has industrial experience in Computer Science (Tartan Laboratories, and ATTAP), Finance (Tudor Investment and PRF, LLC), Robotics and Bio- and Nanotechnologies (Abraxis, OpGen, and Bioarrays). He is editor of Molecular Cancer Therapeutics, AMRX (Applied Mathematics Research Exchange), Nanotechnology, Science and Applications, and Transactions on Systems Biology, and author of a textbook on algorithmic algebra and more than two hundred archived publications. He has advised and mentored more than 35 graduate students and post-docs in the areas of computer science, robotics and control engineering, applied mathematics, finance, biology and medicine. He is an inventor of Optical Mapping and Sequencing (SMASH), Array Mapping, Copy-Number Variation Mapping, Model Checker for circuit verification, Robot Grasping and Fixturing devices and algorithms, Reactive Robotics, and Nanotechnology for DNA profiling. He is a fellow of IEEE, ACM and AAAS, a Distinguished Alumnus of IIT-Kgp, and a NYSTAR Distinguished Professor. He also holds adjunct professorship at Tata Institute of Fundamental Research in Mumbai, India. From 2001-04, he was a professor at the Watson School of Biological Sciences, Cold Spring Harbor Lab; currently he is a QB visiting scholar at Cold Spring Harbor Lab.

Views: 5525
GoogleTechTalks

Lecture 19: Stress
Instructor: John Gabrieli
View the complete course: http://ocw.mit.edu/9-00SCS11
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 15587
MIT OpenCourseWare

In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables. For example,
is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by
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Views: 26
Audiopedia

The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation.
The most important application is in data fitting. The best fit in the least-squares sense minimizes the sum of squared residuals, a residual being the difference between an observed value and the fitted value provided by a model. When the problem has substantial uncertainties in the independent variable (the 'x' variable), then simple regression and least squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.
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Views: 160
Audiopedia

Number theory and the circle packings of Apollonius
Abstract.
Like many problems in number theory, the questions that arise from packing the plane with mutually tangent circles are easy to formulate but difficult to answer. We will explain the basic features of such integral packings and how modern tools from number theory, group theory (symmetries) and combinatorics are being used to answer some of these old questions.
Peter Sarnak is a member of the permanent faculty at the School of Mathematics of the Institute for Advanced Study and has been Eugene Higgins Professor of Mathematics at Princeton University since 2002. He is a member of the National Academy of Sciences (USA) and a Fellow of the Royal Society (UK). He received numerous awards including the Polya Prize (1998) and the Frank Nelson Cole Prize (2005). Professor Sarnak’s interest in mathematics is wide-ranging. He has made major contributions to number theory, analysis, combinatorics and mathematical physics. Professor Sarnak is a colorful and engaging speaker, with a broad and deep command of a wide range of mathematical subjects, and an unsurpassed ability to convey the historical context and the big-picture significance of mathematical ideas.
The Langenhop Lectures are made possible by the generous funding from Carl E. Langenhop, Emeritus Mathematics Professor, SIUC.

Views: 423
SIU Math

The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation.
This video targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Public domain image source in video

Views: 215
encyclopediacc

Dynamic Data Assimilation: an introduction by Prof S. Lakshmivarahan,School of Computer Science,University of Oklahoma.For more details on NPTEL visit http://nptel.ac.in

Views: 1626
nptelhrd

Prof. Stephane Mallat, Professor of Applied Mathematics, Ecole Polytechnique, France
Tutorial

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics
00:00:11 1 19th century
00:04:22 2 20th century
00:04:32 2.1 1900–1909
00:07:55 2.2 1910–1919
00:08:01 2.3 1920–1929
00:12:46 2.4 1930–1939
00:15:16 2.5 1940–1949
00:22:15 2.6 1950–1959
00:30:03 2.7 1960–1969
00:32:44 2.8 1971–1979
00:37:32 2.9 1980–1999
00:45:21 3 21st century
00:49:45 4 See also
00:56:24 5 References
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
"There is only one good, knowledge, and one evil, ignorance."
- Socrates
SUMMARY
=======
This timeline of quantum mechanics shows the key steps, precursors and contributors to the development of quantum mechanics, quantum field theories and quantum chemistry.

Views: 21
Subhajit Sahu

Snow Tha Product - “Nights" (feat. W. Darling)
Download: http://smarturl.it/DownloadNights
Stream: http://smarturl.it/StreamNights
Connect with Snow
https://twitter.com/SnowThaProduct
https://www.facebook.com/SnowThaProduct
https://www.instagram.com/snowthaproduct
https://soundcloud.com/snowthaproduct
http://www.snowthaproduct.com/

Views: 7747019
SNOWTHAPRODUCT

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Linear_subspace
00:00:30 1 Definition
00:02:07 2 Examples
00:02:16 2.1 Example I
00:02:53 2.2 Example II
00:03:10 2.3 Example III
00:03:43 2.4 Example IV
00:04:02 3 Properties of subspaces
00:04:12 4 Descriptions
00:04:48 4.1 Systems of linear equations
00:05:07 4.2 Null space of a matrix
00:05:21 4.3 Linear parametric equations
00:05:38 4.4 Span of vectors
00:06:00 4.5 Column space and row space
00:06:22 4.6 Independence, basis, and dimension
00:06:58 5 Operations and relations on subspaces
00:07:22 5.1 Inclusion
00:08:15 5.2 Intersection
00:08:48 5.3 Sum
00:09:49 5.4 Lattice of subspaces
00:13:20 5.5 Other
00:17:46 6 Algorithms
00:18:43 6.1 Basis for a row space
00:23:54 6.2 Subspace membership
00:29:13 6.3 Basis for a column space
00:30:24 6.4 Coordinates for a vector
00:35:44 6.5 Basis for a null space
00:35:56 6.6 Basis for the sum and intersection of two subspaces
00:36:22 6.7 Equations for a subspace
00:36:38 7 See also
00:36:42 8 Notes
00:38:04 9 Textbooks
00:40:37 10 External links
00:41:10 Other
00:41:54 N ≠ {0}. The same case presents the ⊥ operation in symplectic vector spaces.
00:42:05 Algorithms
00:43:01 Basis for a row space
00:43:58 Subspace membership
00:44:56 Basis for a column space
00:45:58 Coordinates for a vector
00:47:24 Basis for a null space
00:48:13 1 and the remaining free variables are zero. The resulting collection of vectors is a basis for the null space of A.See the article on null space for an example.
00:48:29 Basis for the sum and intersection of two subspaces
00:49:14 Equations for a subspace
00:54:48 See also
00:55:06 Notes
00:55:15 Textbooks
00:58:11 External links
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7552596816803151
Voice name: en-US-Wavenet-A
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space. A linear subspace is usually called simply a subspace when the context serves to distinguish it from other kinds of subspace.

Views: 0
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Frame_(linear_algebra)
00:00:34 1 Definition and motivation
00:00:44 1.1 Motivating example: computing a basis from a linearly dependent set
00:06:22 1.2 Formal definition
00:08:01 1.3 Analysis operator
00:10:28 1.4 Synthesis operator
00:11:46 1.5 Motivation for the lower frame bound
00:14:26 2 History
00:16:08 3 Relation to bases
00:20:37 4 Applications
00:21:54 5 Special cases
00:22:04 5.1 Tight frames
00:22:15 5.2 Equal norm frame
00:22:32 5.3 Equiangular frames
00:24:11 5.4 Exact frames
00:24:49 6 Generalizations
00:25:01 6.1 Continuous Frame
00:25:42 6.1.1 Example
00:26:09 6.1.2 Continuous Analysis Operator
00:26:27 6.1.3 Continuous Synthesis Operator
00:27:25 6.1.4 Continuous Frame Operator
00:29:50 6.1.5 Continuous Dual Frame
00:31:40 7 Dual frames
00:32:44 8 See also
00:34:08 9 Notes
00:36:11 10 References
00:53:54 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7793757295242683
Voice name: en-US-Wavenet-A
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology of signal processing, a frame provides a redundant, stable way of representing a signal. Frames are used in error detection and correction and the design and analysis of filter banks and more generally in applied mathematics, computer science, and engineering..

Views: 1
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Homology_(mathematics)
00:02:34 1 Background
00:02:43 1.1 Origins
00:04:03 1.2 Surfaces
00:08:34 1.3 Generalization
00:08:46 2 Informal examples
00:11:36 3 Construction of homology groups
00:11:48 4 Types of homology
00:15:34 4.1 Simplicial homology
00:20:47 4.2 Singular homology
00:32:37 4.3 Group homology
00:33:10 4.4 Other homology theories
00:37:39 5 Homology functors
00:38:13 6 Properties
00:39:15 7 Applications
00:39:25 7.1 Application in pure mathematics
00:41:15 7.2 Application in science and engineering
00:45:00 8 Software
00:45:10 9 See also
00:46:56 10 Notes
00:49:09 11 References
00:50:21 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.749044202810713
Voice name: en-AU-Wavenet-B
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. Similar constructions are available in a wide variety of other contexts, such as abstract algebra, groups, Lie algebras, Galois theory, and algebraic geometry.
The original motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different kinds of holes. Homology was originally a rigorous mathematical method for defining and categorizing holes in a manifold. Loosely speaking, a cycle is a closed submanifold, a boundary is a cycle which is also the boundary of an (open or closed) submanifold, and a homology class (which represents a hole) is an equivalence class of cycles modulo boundaries. A non-trivial equivalence class is thus represented by a cycle which is not the boundary of any submanifold. A hypothetical manifold whose boundary would be that particular cycle is "not there" which is why that cycle is indicative of the presence of a hole.
There are many different homology theories. A particular type of mathematical object, such as a topological space or a group, may have one or more associated homology theories. When the underlying object has a geometric interpretation like topological spaces do, the nth homology group represents behavior unique to dimension n. In general, most homology groups or modules arise as derived functors on appropriate abelian categories. They provide concrete descriptions of the failure of a functor to be exact. From this abstract perspective, homology groups are determined by objects of a derived category.

Views: 2
wikipedia tts

Dr. Paul E. Sojka is a Professor of Mechanical Engineering specializing in turbulent fluid mechanics.
See an abstract of Dr. Sojka’s talk: https://engineering.purdue.edu/Engr/AboutUs/Administration/AcademicAffairs/Events/Colloquiums/sojka
Watch more colloquia videos: https://engineering.purdue.edu/Engr/AboutUs/Administration/AcademicAffairs/Events/Colloquiums
Learn more about Purdue Engineering: http://engineering.purdue.edu/
Facebook: http://facebook.com/PurdueEngineering
Twitter: https://twitter.com/PurdueEngineers @PurdueEngineers
Contact us: [email protected]
Purdue's College of Engineering is among the largest in the United States and includes 13 academic programs, all with high rankings. U.S. News and World Report ranks Purdue's College of Engineering in the Top 10 nationwide: no. 6 for graduate programs and no. 9 for undergraduate programs, with four schools ranking in the top five for undergraduate programs: Agricultural and Biological Engineering, Civil Engineering, Aeronautics and Astronautics, and Industrial Engineering. Our Agricultural and Biological Engineering (ABE) graduate program has been ranked no.1 for seven consecutive years, and ABE's undergraduate program has been ranked no.1 for five consecutive years.

Views: 306
Purdue Engineering

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem
00:00:51 1 Statement
00:01:42 1.1 Positive matrices
00:02:42 1.2 Non-negative matrices
00:06:33 1.2.1 Classification of matrices
00:08:18 1.2.2 Perron–Frobenius theorem for irreducible matrices
00:11:21 1.3 Further properties
00:14:40 2 Applications
00:17:45 2.1 Non-negative matrices
00:18:07 2.2 Stochastic matrices
00:20:16 2.3 Algebraic graph theory
00:21:00 2.4 Finite Markov chains
00:21:36 2.5 Compact operators
00:22:02 3 Proof methods
00:22:47 3.1 Perron root is strictly maximal eigenvalue for positive (and primitive) matrices
00:23:14 3.1.1 Proof for positive matrices
00:23:49 3.1.2 Lemma
00:24:02 3.2 Power method and the positive eigenpair
00:24:39 3.3 Multiplicity one
00:25:23 3.4 No other non-negative eigenvectors
00:25:54 3.5 Collatz–Wielandt formula
00:28:09 3.6 Perron projection as a limit: iAsupk/sup/rsupk/sup/i
00:31:14 3.7 Inequalities for Perron–Frobenius eigenvalue
00:31:58 3.8 Further proofs
00:32:46 3.8.1 Perron projection
00:32:56 3.8.2 Peripheral projection
00:33:20 3.8.3 Cyclicity
00:34:03 4 Caveats
00:34:16 5 Terminology
00:34:40 6 See also
00:35:02 7 Notes
00:36:18 8 References
00:36:31 8.1 Original papers
00:37:27 8.2 Further reading
00:37:39 Inequalities for Perron–Frobenius eigenvalue
00:40:48 rw and the smallest component of w (say wi) is 1. Then r
00:41:16 (1, 1, ..., 1) and immediately obtains the inequality.
00:41:23 Further proofs
00:41:32 ==== Perron projection
00:42:17 PA
00:42:34 λx then PAx
00:42:45 ρ(A)Px which means Px
00:43:04 1 then it can be decomposed as P ⊕ (1 − P)A so that An
00:43:53 Peripheral projection
00:44:17 1. So we consider the peripheral projection, which is the spectral projection of A corresponding to all the eigenvalues that have modulus ρ(A). It may then be shown that the peripheral projection of an irreducible non-negative square matrix is a non-negative matrix with a positive diagonal.
00:44:34 Cyclicity
00:44:42 Suppose in addition that ρ(A)
00:44:58 AP
00:46:03 R ⊕ (1 − P)A so the difference between An and Rn is An − Rn
00:46:26 Caveats
00:47:54 eiπ/3 then ω6
00:48:12 Terminology
00:49:21 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
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"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
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In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical systems (subshifts of finite type); to economics (Okishio's theorem, Hawkins–Simon condition);
to demography (Leslie population age distribution model);
to social networks (DeGroot learning process), to Internet search engines and even to ranking of football
teams. The first to discuss the ordering of players within tournaments using Perron–Frobenius eigenvectors is Edmund Landau.

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wikipedia tts

My advice is this: Settle! That's right. Don't worry about passion or intense connection. Don't nix a guy based on his annoying habit of yelling "Bravo!" in movie theaters. Overlook his halitosis or abysmal sense of aesthetics. Because if you want to have the infrastructure in place to have a family, settling is the way to go. Based on my observations, in fact, settling will probably make you happier in the long run, since many of those who marry with great expectations become more disillusioned with each passing year. (It's hard to maintain that level of zing when the conversation morphs into discussions about who's changing the diapers or balancing the checkbook.)
Obviously, I wasn't always an advocate of settling. In fact, it took not settling to make me realize that settling is the better option, and even though settling is a rampant phenomenon, talking about it in a positive light makes people profoundly uncomfortable. Whenever I make the case for settling, people look at me with creased brows of disapproval or frowns of disappointment, the way a child might look at an older sibling who just informed her that Jerry's Kids aren't going to walk, even if you send them money. It's not only politically incorrect to get behind settling, it's downright un-American. Our culture tells us to keep our eyes on the prize (while our mothers, who know better, tell us not to be so picky), and the theme of holding out for true love (whatever that is—look at the divorce rate) permeates our collective mentality.
Even situation comedies, starting in the 1970s with The Mary Tyler Moore Show and going all the way to Friends, feature endearing single women in the dating trenches, and there's supposed to be something romantic and even heroic about their search for true love. Of course, the crucial difference is that, whereas the earlier series begins after Mary has been jilted by her fiancé, the more modern-day Friends opens as Rachel Green leaves her nice-guy orthodontist fiancé at the altar simply because she isn't feeling it. But either way, in episode after episode, as both women continue to be unlucky in love, settling starts to look pretty darn appealing. Mary is supposed to be contentedly independent and fulfilled by her newsroom family, but in fact her life seems lonely. Are we to assume that at the end of the series, Mary, by then in her late 30s, found her soul mate after the lights in the newsroom went out and her work family was disbanded? If her experience was anything like mine or that of my single friends, it's unlikely.
And while Rachel and her supposed soul mate, Ross, finally get together (for the umpteenth time) in the finale of Friends, do we feel confident that she'll be happier with Ross than she would have been had she settled down with Barry, the orthodontist, 10 years earlier? She and Ross have passion but have never had long-term stability, and the fireworks she experiences with him but not with Barry might actually turn out to be a liability, given how many times their relationship has already gone up in flames. It's equally questionable whether Sex and the City's Carrie Bradshaw, who cheated on her kindhearted and generous boyfriend, Aidan, only to end up with the more exciting but self-absorbed Mr. Big, will be better off in the framework of marriage and family. (Some time after the breakup, when Carrie ran into Aidan on the street, he was carrying his infant in a Baby Björn. Can anyone imagine Mr. Big walking around with a Björn?)

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Shari Wing

In mathematics, computer science, economics, and bioinformatics, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems and optimal substructure (described below). When applicable, the method takes far less time than naive methods that don't take advantage of the subproblem overlap (like depth-first search).
The idea behind dynamic programming is quite simple. In general, to solve a given problem, we need to solve different parts of the problem (subproblems), then combine the solutions of the subproblems to reach an overall solution. Often when using a more naive method, many of the subproblems are generated and solved many times. The dynamic programming approach seeks to solve each subproblem only once, thus reducing the number of computations: once the solution to a given subproblem has been computed, it is stored or "memo-ized": the next time the same solution is needed, it is simply looked up. This approach is especially useful when the number of repeating subproblems grows exponentially as a function of the size of the input.
This video is targeted to blind users.
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Article text available under CC-BY-SA
Creative Commons image source in video

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