Lectures related to Orthogonal Matrices: Properties and Applications

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

Explores spectral and singular value decompositions of matrices.

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

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

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

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

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

Explores orthogonal diagonalization of symmetric matrices using orthonormal bases and the Gram-Schmidt method.

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

Covers the theorems related to orthogonal projection and orthonormal bases.

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

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

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

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

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

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

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.