Lectures related to Orthogonality and Projection

Covers linear independence, bases, and coordinate systems with examples and theorems.

Covers orthogonal bases, Gram-Schmidt method, linear independence, and orthonormal matrices in vector spaces.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

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

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

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