Symmetric Matrices and Diagonalization

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

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

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

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Covers matrix operations, including multiplication, transposition, powers, and inverses, and explains how to determine if a matrix is invertible.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Introduces symmetric and anti-symmetric matrices, matrix powers, inverses, elementary matrices, and matrix manipulation.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

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

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.