Lectures related to Singular Value Decomposition: Theory and Applications

Explores the Local Inversion Theorem, highlighting conditions for local diffeomorphism and unique solutions in differentiable functions.

Covers the concept of inverse matrices and systems resolution, including the conditions for matrix invertibility and the Gauss-Jordan algorithm.

Covers the integration of rational functions and the decomposition into irreducible factors.

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Explores matrix arithmetic, including properties, products, and dimensions, with a focus on matrix multiplication and commutativity.

Covers the concept of polynomial characteristic of a matrix and its relation to eigenvalues.