Lectures related to Orthogonal Base Change

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

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

Explores the matrix representation of operators and basis transformation in linear algebra.

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

Explores the properties of invertible matrices, including unique solutions and linear independence.

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

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

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

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

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

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

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

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

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

Explores vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.

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

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

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

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

Explores spectral and singular value decompositions of matrices.