Lectures related to Integration of Rational Functions

Explores the decomposition of a function into simple and quadratic factors.

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Covers the integration of simple elements and limit expansions with examples.

Covers the Factorisation QR theorem and the Gram-Schmidt method for orthonormal bases.

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

Covers vector spaces, bases, and decomposition of vectors in R³.

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

Covers the resolution of linear systems and its link to optimization problems.

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

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