Markov Matrices, Steady State, Fourier Series, and Projections
In this lesson on Markov matrices, steady state, Fourier series, and projections, the lecturer explains the properties of Markov matrices and how they are connected to probability ideas. The focus is on eigenvalues and eigenvectors, and the lecture explores the steady state of a system, which corresponds to an eigenvalue of 1 and its eigenvector. The eigenvector has all positive components, and the lecture goes on to discuss the applications of Markov matrices in population movements, such as the populations of California and Massachusetts.
Markov Matrices, Steady State, Fourier Series, and Projections -- Lecture 24a. A lesson all about applications of Eigenvalues and Eigenvectors.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- Fourier Transforms - Laplace, Power Series, and Fourier Transforms
- Fourier Series Java Applet - Java applet to play around to investigate the Fourier Series.
- Trig Series Java Applet - Java applet to play around to investigate trigonometric series, their sums, and how this relates to Fourier Series.
- Gibbs Phenomenon Java Applet - Java applet to play around with to investigate the Gibbs Phenomenon.
- Fourier Series Functions - Fourier Series of the function f(x), Remainder of Fourier series, Riemann's Theorem, Parseval's Theorem, Fourier Transforms, and other functions.
- Markov Chains - A list of several Markov Chain simulations.
- What are some applications of Eigenvalues?
- What is a Markov matrix?
- How do you use a Markov matrix?
- What are Fourier series?
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Staff Review
In this video, we get to see some applications of Eigenvectors and Eigenvalues. They really contribute to some very interesting topics. Markov matrices and Fourier series are really useful in other disciplines that use probability and randomness. Also, they are used in random walk analysis.
