Orthonormal Bases in Hilbert Spaces

Related lectures (30)

Page 3 of 3

Introduces the first step in finding an orthogonal/orthonormal base in a vector space.

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.

Covers the quantization of topological operators and Ising models on square lattices.

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

Explores orthogonal projections, orthonormal bases, and QR factorization in linear algebra.

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

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

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Explores cross-correlation, signal detection, Hilbert spaces, orthogonal approximation, and image compression using DCT.