Lectures related to Linear Algebra: Dot Product and Pre-Hilbertian Spaces

Introduces vector spaces, bases, and the Hilbert space, highlighting the practical implications of defining a basis in a vector space.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Covers vector spaces, differentiable functions, scalar product, and norms in depth.

Covers the concept of inner product spacer and its importance in mathematical contexts.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

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

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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