Spectral Decomposition of Unbounded Operators

Related lectures (51)

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

Covers Hermitian and Unitary operators, real number equivalents, and eigenvalues.

Discusses properties of symmetric matrices and the Spectral Theorem.

Explores quantum mechanics through observables, eigenvalues, and operators.

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

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Explores the Schrödinger equation in quantum mechanics, emphasizing conservation of probability and numerical schemes.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Explores the unique decomposition of matrices into diagonalizable and nilpotent parts, showcasing their properties and applications.

Explores the Heisenberg uncertainty principle, conservation laws, and quantum mechanics properties.

Page 3 of 3