Subspaces, Spectra, and Projections

Related lectures (25)

Page 2 of 3

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

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

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

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

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

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

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.