Jordan Form: Diagonalization and Nilpotent Matrices

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Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Explores the diagonalization of linear maps by finding a basis formed by eigenvectors.

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Explores the diagonalization of symmetric matrices and the importance of Singular Value Decomposition.

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Explores the diagonalization of symmetric matrices using eigenvectors and eigenvalues, emphasizing orthogonality and real eigenvalues.

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.