Lectures related to Orthonormal basis

Projection in Vector Spaces

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

Dirac's Notation, Tensor Product

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Analytical Study of Space

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Orthogonal Bases in Vector Spaces

Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.

Orthonormal Bases in Hilbert Spaces

Explores orthonormal bases in Hilbert spaces, discussing their properties and generation using the Gram-Schmidt method.

Analytical Study of Space

Covers the analytical study of space, focusing on points, lines, and planes.

Singular Value Decomposition: Fundamentals and Applications

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.

Symmetric Matrices: Diagonalizability and Eigenvectors

Explores the diagonalizability of symmetric matrices and their eigenvectors in an orthonormal basis.