Lectures related to Orthogonal Diagonalization

Diagonalisation of Symmetric Matrix by Orthogonal Matrix

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

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Singular Value Decomposition: Applications and Interpretation

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

Diagonalization of Symmetric Matrices

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

Diagonalization in Symmetric Matrices

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

Symmetric Matrices and Orthogonal Matrices

Covers the properties of symmetric matrices, orthogonal matrices, and eigenvalues.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Eigenvalues and Eigenvectors Decomposition

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

Orthogonal Base Change

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

Orthogonal Matrices & Spectral Decomposition

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.

Orthogonal Matrices: Properties and Applications

Covers the properties and applications of orthogonal matrices.

Calcul de valeurs propres

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Spectral Theorem Recap

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

Matrix Decomposition: Triangular and Spectral

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

Diagonalization of Symmetric Matrices

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

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Symmetric Matrices: Diagonalizability and Eigenvectors

Explores the diagonalizability of symmetric matrices and their eigenvectors in an orthonormal basis.

Spectral Decomposition and SVD

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