Lectures related to Eisenstein Series: Decomposition and Unitarizability

Explains orthogonal families, bases, and projections in vector spaces.

Covers the theorems related to orthogonal projection and orthonormal bases.

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

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

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Explores the uniqueness and properties of orthogonal projection, including decomposition, associated matrix, linearity, and practical examples.

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores symmetrical bilinear forms, the Pythagorean theorem, inequalities, and orthogonal matrices.

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.

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

Covers the QR factorization of a matrix A into Q and R.

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

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Explores orthogonal projections, orthonormal bases, and QR factorization in linear algebra.

Explores QR factorization, orthogonal bases, and matrices for numerical computations and solving systems of equations.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

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

Explores orthogonal projections and the Gram-Schmidt method for constructing bases.

Explores spectral and singular value decompositions of matrices.