Eigenvalue problem: Eigenbasis, Spectral theorem

Related lectures (32)

Page 3 of 4

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Covers the basics of quantum mechanics, focusing on Hamiltonian operator and Schrödinger equations.

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Discusses the existence of a common orthonormal eigenbasis to normal operators.

Covers the proof of unitary group uniqueness and spectral types.

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.