Markov Matrices, Steady State, Fourier Series, and Projections

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Taught by OCW
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Lesson Summary:

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.

Lesson Description:

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), (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
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Questions answered by this video:
  • What are some applications of Eigenvalues?
  • What is a Markov matrix?
  • How do you use a Markov matrix?
  • What are Fourier series?
  • Staff Review

    • Currently 4.0/5 Stars.
    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.