Lecture 21: Eigenvalues and eigenvectors
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Eigenvalues and eigenvectors The subject of eigenvalues and eigenvectors will take up most of the rest of the course. We will again be working with square matrices. Eigenvalues are special numbers associated with a matrix and eigenvectors are special vectors. Eigenvectors and eigenvalues A matrix A acts on vectors x like a function does, with input x and output Ax. Eigenvectors are vectors for which Ax is parallel to x. In other words: Ax = λx. In this equation, x is an eigenvector of A and λ is an eigenvalue of A. Eigenvalue 0 If the eigenvalue λ…
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