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HomeMIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018Lecture 4: Eigenvalues and Eigenvectors
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
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Lecture 4: Eigenvalues and Eigenvectors
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Lecture 5: Positive Definite and Semidefinite Matrices
Description
Professor Strang begins this lecture talking about eigenvectors and eigenvalues and why they are useful. Then he moves to a discussion of symmetric matrices, in particular, positive definite matrices.
Summary\(Ax =\) eigenvalue times \(x\)
\(A^2x =\) (eigenvalue)\(^2\) times \(x\)
Write other vectors as combinations of eigenvectors
Similar matrix \(B = M^{-1}AM\) has the same eigenvalues as \(A\)
Related section in textbook: I.6
Instructor: Prof. Gilbert Strang
