Lecture

Symmetric Matrices: Diagonalizability and Eigenvectors

Description

This lecture covers the properties of symmetric matrices, focusing on the theorem stating that a matrix is symmetric if and only if it is diagonalizable in an orthonormal basis. The spectral theorem for symmetric matrices is also discussed, highlighting that such matrices have real eigenvalues, may not be distinct, and can be diagonalized in an orthonormal basis with orthogonal eigenvectors.

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