Lectures related to Invariant subspace

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.

Covers vector subspaces in R3, stability under operations, classification, and properties.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Covers the concept of the sum of vector subspaces in an IR-vector space.

Covers the concept of orthogonal complement in Rn and related propositions and theorems.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Explores the concept of orthogonal complement in vector subspaces and fundamental matrix subspaces.

Covers PCA, finding directions of largest variance, data dimensionality reduction, and limitations of PCA.