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Eigenvalues and Eigenvectors
This lecture introduces the concept of eigenvalues and eigenvectors for square matrices. Eigenvalues are values for which a matrix times a vector equals a scalar times the same vector. Eigenvectors are the vectors associated with eigenvalues. The lecture covers definitions, examples, consequences, and calculations of eigenvalues and eigenvectors, as well as characteristic polynomials. It also explains how to find eigenspaces associated with eigenvalues and provides examples of finding eigenspaces for different matrices.
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