Lectures related to Integration of Rational Functions

Covers notations, operations, isomorphism, and polar decomposition of complex numbers.

Covers complete and orthonormal families in a Hilbert space, discussing unique projections and vector decomposition.

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

Explains the QR factorization theorem and demonstrates the Gram-Schmidt procedure with an example.

Covers the Fourier series representation of periodic signals and harmonic analysis.

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

Covers bases, transformations, and matrix decompositions in linear algebra.

Introduces the argument of complex numbers and the polar method, demonstrating their application in finding roots.