Orthogonal Matrices & Spectral Decomposition

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Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Diagonalization in Symmetric Matrices

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

Diagonalization of Symmetric Matrices

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

SVD: Singular Value Decomposition

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices and the orthogonality of eigenvectors.

Orthogonal Base Change

Explores orthogonal base change in linear algebra, focusing on matrices and transformations.

Eigenvalues and Eigenvectors Decomposition

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

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Linear Algebra: Singular Value Decomposition

Delves into singular value decomposition and its applications in linear algebra.

Diagonalisation of Symmetric Matrix by Orthogonal Matrix

Covers the method of diagonalizing a symmetric matrix using an orthogonal matrix.