Podcasts about eigenvalues

In this week's episode Greg and Patrick shine a flashlight on correspondence analysis and find that this is an extraordinarily cool yet often neglected method similar to factor analysis but applied to nominal contingency tables. Along the way they also discuss online personality tests, marital therapy, modern antibiotics, the Newlywed Game, grand slams, the advantages of being flexible, disrespecting nominal variables, formally apologizing to linguists, Winnie the Pooh, VH1's Pop-Up Video, the witches of Macbeth, Wait Wait Don't Tell Me, and the downsides of Novocaine. Stay in contact with Quantitude! Web page: quantitudepod.org TwitterX: @quantitudepod YouTube: @quantitudepod Merch: redbubble.com

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: An Extremely Opinionated Annotated List of My Favourite Mechanistic Interpretability Papers v2, published by Neel Nanda on July 7, 2024 on The AI Alignment Forum. This post represents my personal hot takes, not the opinions of my team or employer. This is a massively updated version of a similar list I made two years ago There's a lot of mechanistic interpretability papers, and more come out all the time. This can be pretty intimidating if you're new to the field! To try helping out, here's a reading list of my favourite mech interp papers: papers which I think are important to be aware of, often worth skimming, and something worth reading deeply (time permitting). I've annotated these with my key takeaways, what I like about each paper, which bits to deeply engage with vs skim, etc. I wrote a similar post 2 years ago, but a lot has changed since then, thus v2! Note that this is not trying to be a comprehensive literature review - this is my answer to "if you have limited time and want to get up to speed on the field as fast as you can, what should you do". I'm deliberately not following academic norms like necessarily citing the first paper introducing something, or all papers doing some work, and am massively biased towards recent work that is more relevant to the cutting edge. I also shamelessly recommend a bunch of my own work here, sorry! How to read this post: I've bolded the most important papers to read, which I recommend prioritising. All of the papers are annotated with my interpretation and key takeaways, and tbh I think reading that may be comparable good to skimming the paper. And there's far too many papers to read all of them deeply unless you want to make that a significant priority. I recommend reading all my summaries, noting the papers and areas that excite you, and then trying to dive deeply into those. Foundational Work A Mathematical Framework for Transformer Circuits (Nelson Elhage et al, Anthropic) - absolute classic, foundational ideas for how to think about transformers (see my blog post for what to skip). See my youtube tutorial (I hear this is best watched after reading the paper, and adds additional clarity) Deeply engage with: All the ideas in the overview section, especially: Understanding the residual stream and why it's fundamental. The notion of interpreting paths between interpretable bits (eg input tokens and output logits) where the path is a composition of matrices and how this is different from interpreting every intermediate activations And understanding attention heads: what a QK and OV matrix is, how attention heads are independent and additive and how attention and OV are semi-independent. Skip Trigrams & Skip Trigram bugs, esp understanding why these are a really easy thing to do with attention, and how the bugs are inherent to attention heads separating where to attend to (QK) and what to do once you attend somewhere (OV) Induction heads, esp why this is K-Composition (and how that's different from Q & V composition), how the circuit works mechanistically, and why this is too hard to do in a 1L model Skim or skip: Eigenvalues or tensor products. They have the worst effort per unit insight of the paper and aren't very important. Superposition Superposition is a core principle/problem in model internals. For any given activation (eg the output of MLP13), we believe that there's a massive dictionary of concepts/features the model knows of. Each feature has a corresponding vector, and model activations are a sparse linear combination of these meaningful feature vectors. Further, there are more features in the dictionary than activation dimensions, and they are thus compressed in and interfere with each other, essentially causing cascading errors. This phenomena of compression is called superposition. Toy models of superpositio...

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Math-to-English Cheat Sheet, published by nahoj on April 9, 2024 on LessWrong. Say you've learnt math in your native language which is not English. Since then you've also read math in English and you appreciate the near universality of mathematical notation. Then one day you want to discuss a formula in real life and you realize you don't know how to pronunce "an". Status: I had little prior knowledge of the topic. This was mostly generated by ChatGPT4 and kindly reviewed by @TheManxLoiner. General Distinguishing case F,δ "Big F" or "capital F", "little delta" Subscripts an "a sub n" or, in most cases, just "a n" Calculus Pythagorean Theorem a2+b2=c2 "a squared plus b squared equals c squared." Area of a Circle A=πr2 "Area equals pi r squared." Slope of a Line m=y2y1x2x1 "m equals y 2 minus y 1 over x 2 minus x 1." Quadratic Formula x=bb24ac2a "x equals minus b [or 'negative b'] plus or minus the square root of b squared minus four a c, all over two a." Sum of an Arithmetic Series S=n2(a1+an) "S equals n over two times a 1 plus a n." Euler's Formula eiθ=cos(θ)+isin(θ) "e to the i theta equals cos [pronounced 'coz'] theta plus i sine theta." Law of Sines sin(A)a=sin(B)b=sin(C)c "Sine A over a equals sine B over b equals sine C over c." Area of a Triangle (Heron's Formula) A=s(sa)(sb)(sc), where s=a+b+c2 "Area equals the square root of s times s minus a times s minus b times s minus c, where s equals a plus b plus c over two." Compound Interest Formula A=P(1+rn)nt "A equals P times one plus r over n to the power of n t." Logarithm Properties logb(xy)=logb(x)+logb(y) Don't state the base if clear from context: "Log of x y equals log of x plus log of y." Otherwise "Log to the base b of x y equals log to the base b of x plus log to the base b of y." More advanced operations Derivative of a Function dfdx or ddxf(x) or f'(x) "df by dx" or "d dx of f of x" or "f prime of x." Second Derivative d2dx2f(x) or f''(x) "d squared dx squared of f of x" or "f double prime of x." Partial Derivative (unreviewed) xf(x,y) "Partial with respect to x of f of x, y." Definite Integral baf(x)dx "Integral from a to b of f of x dx." Indefinite Integral (Antiderivative) f(x)dx "Integral of f of x dx." Line Integral (unreviewed) Cf(x,y)ds "Line integral over C of f of x, y ds." Double Integral badcf(x,y)dxdy "Double integral from a to b and c to d of f of x, y dx dy." Gradient of a Function f "Nabla f" or "gradient of f" to distinguish from other uses such as divergence or curl. Divergence of a Vector Field F "Nabla dot F." Curl of a Vector Field F "Nabla cross F." Laplace Operator (unreviewed) Δf or 2f "Delta f" or "Nabla squared f." Limit of a Function limxaf(x) "Limit as x approaches a of f of x." Linear Algebra (vectors and matrices) Vector Addition v+w "v plus w." Scalar Multiplication cv "c times v." Dot Product vw "v dot w." Cross Product vw "v cross w." Matrix Multiplication AB "A B." Matrix Transpose AT "A transpose." Determinant of a Matrix |A| or det(A) "Determinant of A" or "det A". Inverse of a Matrix A1 "A inverse." Eigenvalues and Eigenvectors λ for eigenvalues, v for eigenvectors "Lambda for eigenvalues; v for eigenvectors." Rank of a Matrix rank(A) "Rank of A." Trace of a Matrix tr(A) "Trace of A." Vector Norm v "Norm of v" or "length of v". Orthogonal Vectors vw=0 "v dot w equals zero." With numerical values Matrix Multiplication with Numerical Values Let A=(1234) and B=(5678), then AB=(19224350). "A B equals nineteen, twenty-two; forty-three, fifty." Vector Dot Product Let v=(1,2,3) and w=(4,5,6), then vw=32. "v dot w equals thirty-two." Determinant of a Matrix For A=(1234), |A|=2. "Determinant of A equals minus two." Eigenvalues and Eigenvectors with Numerical Values Given A=(2112), it has eigenvalues λ1=3 and λ2=1, with corresponding eigenvectors v1=(11) and v2=(11). "Lambda ...

Link to original articleWelcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Math-to-English Cheat Sheet, published by nahoj on April 9, 2024 on LessWrong. Say you've learnt math in your native language which is not English. Since then you've also read math in English and you appreciate the near universality of mathematical notation. Then one day you want to discuss a formula in real life and you realize you don't know how to pronunce "an". Status: I had little prior knowledge of the topic. This was mostly generated by ChatGPT4 and kindly reviewed by @TheManxLoiner. General Distinguishing case F,δ "Big F" or "capital F", "little delta" Subscripts an "a sub n" or, in most cases, just "a n" Calculus Pythagorean Theorem a2+b2=c2 "a squared plus b squared equals c squared." Area of a Circle A=πr2 "Area equals pi r squared." Slope of a Line m=y2y1x2x1 "m equals y 2 minus y 1 over x 2 minus x 1." Quadratic Formula x=bb24ac2a "x equals minus b [or 'negative b'] plus or minus the square root of b squared minus four a c, all over two a." Sum of an Arithmetic Series S=n2(a1+an) "S equals n over two times a 1 plus a n." Euler's Formula eiθ=cos(θ)+isin(θ) "e to the i theta equals cos [pronounced 'coz'] theta plus i sine theta." Law of Sines sin(A)a=sin(B)b=sin(C)c "Sine A over a equals sine B over b equals sine C over c." Area of a Triangle (Heron's Formula) A=s(sa)(sb)(sc), where s=a+b+c2 "Area equals the square root of s times s minus a times s minus b times s minus c, where s equals a plus b plus c over two." Compound Interest Formula A=P(1+rn)nt "A equals P times one plus r over n to the power of n t." Logarithm Properties logb(xy)=logb(x)+logb(y) Don't state the base if clear from context: "Log of x y equals log of x plus log of y." Otherwise "Log to the base b of x y equals log to the base b of x plus log to the base b of y." More advanced operations Derivative of a Function dfdx or ddxf(x) or f'(x) "df by dx" or "d dx of f of x" or "f prime of x." Second Derivative d2dx2f(x) or f''(x) "d squared dx squared of f of x" or "f double prime of x." Partial Derivative (unreviewed) xf(x,y) "Partial with respect to x of f of x, y." Definite Integral baf(x)dx "Integral from a to b of f of x dx." Indefinite Integral (Antiderivative) f(x)dx "Integral of f of x dx." Line Integral (unreviewed) Cf(x,y)ds "Line integral over C of f of x, y ds." Double Integral badcf(x,y)dxdy "Double integral from a to b and c to d of f of x, y dx dy." Gradient of a Function f "Nabla f" or "gradient of f" to distinguish from other uses such as divergence or curl. Divergence of a Vector Field F "Nabla dot F." Curl of a Vector Field F "Nabla cross F." Laplace Operator (unreviewed) Δf or 2f "Delta f" or "Nabla squared f." Limit of a Function limxaf(x) "Limit as x approaches a of f of x." Linear Algebra (vectors and matrices) Vector Addition v+w "v plus w." Scalar Multiplication cv "c times v." Dot Product vw "v dot w." Cross Product vw "v cross w." Matrix Multiplication AB "A B." Matrix Transpose AT "A transpose." Determinant of a Matrix |A| or det(A) "Determinant of A" or "det A". Inverse of a Matrix A1 "A inverse." Eigenvalues and Eigenvectors λ for eigenvalues, v for eigenvectors "Lambda for eigenvalues; v for eigenvectors." Rank of a Matrix rank(A) "Rank of A." Trace of a Matrix tr(A) "Trace of A." Vector Norm v "Norm of v" or "length of v". Orthogonal Vectors vw=0 "v dot w equals zero." With numerical values Matrix Multiplication with Numerical Values Let A=(1234) and B=(5678), then AB=(19224350). "A B equals nineteen, twenty-two; forty-three, fifty." Vector Dot Product Let v=(1,2,3) and w=(4,5,6), then vw=32. "v dot w equals thirty-two." Determinant of a Matrix For A=(1234), |A|=2. "Determinant of A equals minus two." Eigenvalues and Eigenvectors with Numerical Values Given A=(2112), it has eigenvalues λ1=3 and λ2=1, with corresponding eigenvectors v1=(11) and v2=(11). "Lambda ...

I read from Egyptian to eigenvector.     Egypt https://en.wikipedia.org/wiki/Egypt     Technically, yes, Mammoths were still around while the pyramids were being built, but it was a small population on an island.  https://www.worldatlas.com/articles/did-woolly-mammoths-still-roam-parts-of-earth-when-the-great-pyramids-were-built.html     The fantastic podcast "Ologies" by Alie Ward has a great episode about Egyptian bread called "Gastroegyptology" https://www.alieward.com/ologies/gastroegyptology     Eigenvalues and eigenvectors, oh my! https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors     The word of the episode is "eidetic". https://en.wikipedia.org/wiki/Eidetic_memory     Theme music from Jonah Kraut https://jonahkraut.bandcamp.com/     Merchandising! https://www.teepublic.com/user/spejampar     "The Dictionary - Letter A" on YouTube   "The Dictionary - Letter B" on YouTube   "The Dictionary - Letter C" on YouTube   "The Dictionary - Letter D" on YouTube     Featured in a Top 10 Dictionary Podcasts list! https://blog.feedspot.com/dictionary_podcasts/     Backwards Talking on YouTube: https://www.youtube.com/playlist?list=PLmIujMwEDbgZUexyR90jaTEEVmAYcCzuq     dictionarypod@gmail.com https://www.facebook.com/thedictionarypod/ https://www.threads.net/@dictionarypod https://twitter.com/dictionarypod https://www.instagram.com/dictionarypod/ https://www.patreon.com/spejampar https://www.tiktok.com/@spejampar 917-727-5757

Stephen Wolfram answers general questions from his viewers about science and technology as part of an unscripted livestream series, also available on YouTube here: https://wolfr.am/youtube-sw-qa Questions include: Why do flies fly around seemingly constantly with no apparent goal whatsoever? - Why don't we make houses out of some kind of amber and then carve them? - How do traffic light systems work? - Does Stephen prepare any of the answers? they are all so clear and thought out - Hello, how are the magnetic north and geographical north related? - 1 How come oil is deposited in Arctic regions? - Could you please explain what Eigenvalues/vectors and what you can do with them. Thanks.

In this week's episode Greg and Patrick continue their discussion from last week in The Mättrix Part Deux, exploring the magic of matrices including estimation, eigenvalues, and eigenvectors. Along the way they also mention flawed audio transcripts, 50 Shades of Greg, drunkenly shoving a matrix, drug mules, things you need, isomorphic interdigitation, plywood and tennis balls, heroin-filled condoms, talking to volleyballs, bawitdaba da bang a dang diggy diggy, meat grinders, not going to prom, vector bouquets, and The Wright Stuff.  

Michael Levitin; University of Reading 23 May 2007 – 11:00 to 12:00

In this episode I tried to explain the principle behind face regonition using PCA -Eigen face Approach PCA- Principal Component Analysis Eigen faces: An eigenface is the name given to a set of eigenvectors when used in the computer vision problem of human face recognition. What is eigenvalues and eigenvectors in PCA? Eigenvectors are unit vectors with length or magnitude equal to 1. ... Eigenvalues are coefficients applied to eigenvectors that give the vectors their length or magnitude. Covariance Matrix:is a square matrix giving the covariance between each pair of elements of a given random vector. Listen the episode on all podcast platform and share your feedback as comments here Do check the episode on various platform follow me on instagram https://www.instagram.com/podcasteramit Apple https://podcasts.apple.com/us/podcast/id1544510362 Huhopper Platform https://hubhopper.com/podcast/tech-stories/318515 Amazon https://music.amazon.com/podcasts/2fdb5c45-2016-459e-ba6a-3cbae5a1fa4d Spotify https://open.spotify.com/show/2GhCrAjQuVMFYBq8GbLbwa

Okay enough messing around, this week we get into the Matrix. Okay not that matrix. The mathematical matrix. But this one is way more powerful than a dystopian future in which humanity is unknowingly trapped inside a simulated reality. That's piddly. Mathematical matrices are used in everywhere, from making computer games to quantum physics.That's Jane Breen ,Assistant Professor in Applied Maths in Ontario University in Canada. She loves modelling the complexity of networks in the real world with some very powerful and sometimes simple tools. Speaking of simple tools, before long, I start throw around lingo like Eigenvalues and Markov Chains like I know what I'm talking about. We find out how Google got so successful, a brief digression into how drugmakers know their drugs will work and before finishing off on how to control the spread of disease. And Ruby and Lily find themselves playing with a real-life application of a Markov Chain, a Game of Snakes and Ladders. Jane Breen https://sites.google.com/view/breenjA really good youtube channel for visualising what's going on in Matrices and All Of That. https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

Today we're going to cover a computer programming language many might not have heard of, ALGOL.  ALGOL was written in 1958. It wasn't like many of the other languages in that it was built by committee. The Association for Computing Machinery and the German Society of Applied Mathematics and Mechanics were floating around ideas for a universal computer programming language.  Members from the ACM were a who's who of people influential in the transition from custom computers that were the size of small homes to mainframes. John Backus of IBM had written a programming language called Speedcoding and then Fortran. Joseph Wegstein had been involved in the development of COBOL. Alan Perlis had been involved in Whirlwind and was with the Carnegie Institute of Technology. Charles Katz had worked with Grace Hopper on UNIVAC and FLOW-MATIC.  The Germans were equally as influential. Frederich Bauer had brought us the stack method while at the Technical University of Munich. Hermann Bottenbruch from The Institute for Applied Mathematics had written a paper on constructing languages. Klaus Samelson had worked on a computer called PERM that was similar to the MIT Whirlwind project. He'd come into computing while studying Eigenvalues.  Heinz Ritishauser had written a number of papers on programming techniques and had codeveloped the language Superplan while at the The Swiss Federal Institute of Technology. This is where the meeting would be hosted. They went from May 27th to June 2nd in 1958 and initially called the language they would develop as IAL, or the International Algebraic Language. But would expand the name to ALGOL, short for Algorithmic Language. They brought us code blocks, the concept that you have a pair of words or symbols that would begin and end a stanza of code, like begin and end. They introduced nested scoped functions. They wrote the whole language right there. You would name a variable by simply saying integer or setting the variable as a := 1. You would substantiate a for and define the steps to perform until - the root of what we would now call a for loop. You could read a variable in from a punch card. It had built-in SIN and COSIN. It was line based and fairly simple functional programming by today's standards. They defined how to handle special characters, built boolean operators, floating point notation. It even had portable types.  And by the end had a compiler that would run on the Z22 computer from Konrad Zuse. While some of Backus' best work it effectively competed with FORTRAN and never really gained traction at IBM. But it influenced almost everything that happened afterwards.  Languages were popping up all over the place and in order to bring in more programmers, they wanted a formalized way to allow languages to flourish, but with a standardized notation system so algorithms could be published and shared and developers could follow along with logic. One outcome of the ALGOL project was the Backus–Naur form, which was the first such standardization. That would be expanded by Danish Peter Naur for ALGOL 60, thus the name. In ALGOL 60 they would meet in Paris, also adding Father John McCarthy, Julien Green, Bernard Vauquois, Adriaan van Wijngaarden, and Michael Woodger. It got refined, yet a bit more complicated. FORTRAN and COBOL use continued to rage on, but academics loved ALGOL. And the original implementation now referred to as the ZMMD implementation, gave way to X1 ALGOL, Case ALGOL, ZAM in Poland, GOGOL, VALGOL, RegneCentralen ALGOL, Whetstone ALGOL for physics, Chinese ALGOL, ALGAMS, NU ALGOL out of Norway, ALGEK out of Russia,  Dartmouth ALGOL, DG/L, USS 90 Algol, Elliot ALGOL, the ALGOL Translator, Kidsgrove Algol, JOVIAL, Burroughs ALGOL, Niklaus Firths ALGOL W, which led to Pascal, MALGOL, and the last would be S-algol in 1979.  But it got overly complicated and overly formal. Individual developers wanted more flexibility here and there. Some wanted simpler languages. Some needed more complicated languages. ALGOL didn't disappear as much as it evolved into other languages. Those were coming out fast and with a committee to approve changes to ALGOL, they were much slower to iterate.  You see, ALGOL profoundly shaped how we think of programming languages. That formalization was critical to paving the way for generations of developers who brought us future languages. ALGOL would end up being the parent of CPL and through CPL, BCPL, C, C++, and through that Objective-C. From ALGOL also sprang Simula and through Simula, Smalltalk. And Pascal and from there, Modula and Delphi. It was only used for a few years but it spawned so much of what developers use to build software today.  In fact, other languages evolved as anti-ALGOL-derivitives, looking at how you did something and deciding to do it totally differently.  And so we owe this crew our thanks. They helped to legitimize a new doctrine, a new career, computer programmer. They inspired. They coded. And in so doing, they helped bring us into the world of functional programming and set structures that allowed the the next generation of great thinkers to go even further, directly influencing people like Adele Goldberg and Alan Kay.  And it's okay that the name of this massive contribution is mostly lost to the annals of history. Because ultimately, the impact is not. So think about this - what can we do to help shape the world we live in? Whether it be through raw creation, iteration, standardization, or formalization - we all have a role to play in this world. I look forward to hearing more about yours as it evolves!

In this Episode we talked about the deep neural networks and the spectral density of each layer's weights. It turns out, you can predict the accuracy ( and many more) with the WeigthWatcher application. We talk about the 5+1 Phases of learning and Heavy Tailed Self Regularization. Charles Martin, PhD on LinkedIn: https://www.linkedin.com/in/charlesmartin14/ During the episode we talked about these VC Theory: https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_theory Why Deep Learning works? post by Charles Martin, 2015 https://calculatedcontent.com/2015/03/25/why-does-deep-learning-work/ Presentation at Berkeley: Why Deep Learning works? by Charles Martin, 2016 https://www.youtube.com/watch?v=fHZZgfVgC8U Several Papers written by Charles Martin and Michael Mahoney: https://arxiv.org/search/?query=%22Charles+H.+Martin%22&searchtype=author&abstracts=show&order=-announced_date_first&size=50 Newest blog post about weightwatcher, 2019 December: https://calculatedcontent.com/2019/12/03/towards-a-new-theory-of-learning-statistical-mechanics-of-deep-neural-networks/ WeightWatcher on GitHub: https://github.com/CalculatedContent/WeightWatcher easy installation for python users: pip install weightwatcher How to reach out: https://calculationconsulting.com/ charles@calculationconsulting.com To access their slack channel please contact Charles first. ---Copyright Info--- Music is from https://filmmusic.io , intro first part is by Miklos Toth and some free garage band loops. :) intro second part: "Aces High" by Kevin MacLeod, outro "Acid Trumpet" by Kevin MacLeod (https://incompetech.com), License: CC BY (http://creativecommons.org/licenses/by/4.0/)  

A teaching assistant works through a problem on eigenvalues and eigenvectors.

I'm joined this week by social marketing master, Taylor Nikolai, who thinks I don't pronounce his name correctly. Taylor drops some wisdom in the form of Gamification Theory when it comes to education, so much like how Pokemon Go has gamified exercise, he thinks the same can be done with education as a whole. Look forward to solving for Eigenvalues in the next Dark Souls! I also witnessed the start of a race war on my street. I brought in the clip of a black guy (who we come to learn is half-Mexican) going toe-to-toe with a Mexican delivery man. Who wins? You, the listener, because I recorded the entire thing. Plus Rucka is back and pleased to hear all our new Italian and Armenian callers. Also, here is a quick survey to help out the show: http://survey.libsyn.com/madcastmedia We also discuss whether Snoop Dog should be culpable for encouraging his fans to rush the stage, which caused it to collapse. And as promised, here's that hot Corvette mom. Is it just me? https://rss.madcastmedia.com/bestdebate/10/ Stone fox. Correction: Her knuckle tattoos say: "FEAR - LESS." Badass. The voicemail number is: 1-562-58-I-RULE (1-562-584-7853). madcastmedia.com Sources Washington Post - Why Bernie Sanders' free college plan doesn't make sense - https://www.washingtonpost.com/news/grade-point/wp/2016/04/22/why-bernie-sanderss-free-college-plan-doesnt-make-sense/ Education.com - Waiting for Superman: cost of high school drop out - http://www.education.com/magazine/article/waiting-superman-means-parents/ KRON4 - Mom stuffed her kids in trunk of Corvette - http://kron4.com/2016/07/18/mom-accused-of-putting-kids-ages-3-and-5-in-corvette-trunk/ LA Times - Snoop Dog concert stage collapses - http://www.latimes.com/entertainment/music/la-et-ms-snoop-dog-concert-injuries-20160806-snap-story.html "Mining by Moonlight" and "Music to Delight" by Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 http://creativecommons.org/licenses/by/3.0/

Two equations with a constant matrix are stable (solutions approach zero) when the trace is negative and the determinant is positive.

Symmetric matrices have n perpendicular eigenvectors and n real eigenvalues.

The eigenvectors remain in the same direction when multiplied by the matrix. Subtracting an eigenvalue from the diagonal leaves a singular matrix: determinant zero. An n by n matrix has n eigenvalues.

Shcherbina, M (Institute for Low Temperatures, Kharkov) Monday 22 June 2015, 15:00-16:00

This lecture covers eigenvalues and eigenvectors of the transition matrix and the steady-state vector of Markov chains. It also includes an analysis of a 2-state Markov chain and a discussion of the Jordan form.

Kiwan, R (A. U. Dubaï) Wednesday 13 May 2015, 15:15-16:00

Rozenblum, G (Chalmers University of Technology) Tuesday 28 April 2015, 15:00-16:00

Shargorodsky, E (King's College London) Tuesday 03 March 2015, 14:00-15:00

Morozov, S (Ludwig-Maximilians-Universität München) Wednesday 25 February 2015, 14:00-15:00

Seri, M (University College London) Tuesday 24 February 2015, 14:00-15:00

Eigenvalues of a 3 by 3 matrix are calculated. Some useful advice is given concerning factorization of the characteristic equation.

We show how to find eigenvalues for an NxN matrix then do a 2x2 example. This MathsCast follows from an introductory MathsCast on eigenvalues and eigenvectors and it is also helpful to view the presentations on linear dependence and independence first.

Explains graphically what it means to multiply a matrix and a vector. Then introduces eigenvectors as vectors belonging to the matrix with a special property in matrix vector multiplication. Eigenvalues are also explained in this context.

Cakoni, F (University of Delaware) Wednesday 03 August 2011, 16:00-16:45

Colton, D (University of Delaware) Wednesday 03 August 2011, 14:00-14:45

Sylvester, J (University of Washington) Tuesday 02 August 2011, 11:15-12:00

This unit is intended to further develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in solving systems of differential equations, this unit assumes that you have some understanding of eigenvalues and eigenvectors. This study unit is just one of many that can be found on LearningSpace, part of OpenLearn, a collection of open educational resources from The Open University. Published in ePub 2.0.1 format, some feature such as audio, video and linked PDF are not supported by all ePub readers.

Goldsheid, I (QMUL) Tuesday 19 August 2008, 15:30-16:30 Anderson Localization and Related Phenomena

Klein, A (UC, Irvine) Tuesday 19 August 2008, 09:00-10:00 Anderson Localization and Related Phenomena

Molchanov, S (North Carolina) Thursday 31 July 2008, 14:00-15:00

Parnovski, L (University College London) Friday 13 April 2007, 14:00-15:00 Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures

Solomyak, M (Weizmann Institute of Science) Thursday 12 April 2007, 15:30-16:30 Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures

Levitin, M (Heriot-Watt) Thursday 12 April 2007, 11:30-12:30 Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures