Diagonalizing a matrix and Powers of A
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Lesson Description:
Diagonalizing a matrix and Powers of A -- Lecture 22. Learn how to diagonalize a matrix and find Eigenvalues for powers of a matrix A.
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
Additional Resources:
- Powers A^n Demo - Demonstration of finding Powers A^nV, which lead toward the top eigenvalue / eigenvector.
- Power Method Applet - Power Method Java applet, which was used in the demo, for you to play around with.
- Diagonalization Mini-Lecture - This is a mini-lecture demo lesson on Diagonalization.
- Powers Mini-Lecture - This is a mini-lecture demo lesson on Powers.
Questions answered by this video:
- How do you diagonalize a matrix?
- How do you find powers of a matrix A?
- What are the Eigenvalues of A squared?
- What are the Eigenvalues of A^2?
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Staff Review
This lecture begins to explain why Eigenvalues are useful. You will learn how to diagonalize a matrix using Eigenvalues and Eigenvectors, and how to use them by taking a matrix A to a power. An interesting and powerful video.
