Lectures related to Subspace-based approximations

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

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

Explains orthogonal bases in R^2 and how to perform orthogonal projections.

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Covers the concept of orthogonal complement and projection in vector spaces.

Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.