Lectures related to Sylvester's Theorem: Orthogonal Bases

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.

Matrix Operations and Orthogonality

Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.

Orthogonal Families & Projections

Covers orthogonal families and projections in vector spaces, including the Gram-Schmidt process.

Linear Algebra in Dirac Notation

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Linear Algebra: Vector Spaces and Linear Independence

Covers vector spaces, operations, and linear independence with examples from polynomials and functions.