Functional Analysis I

Related lectures (29)

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Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Explores the spectral theorem for operators in a Hilbert space.

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

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

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Introduces linear and bounded operators, compact operators, and the Banach space.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

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