Concept

Spectral theorem

Related lectures (31)

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Covers the estimation of time series models and spectral analysis in depth.

Covers the diagonalization of symmetric matrices and the spectral theorem.

Spectral Theory: Regularity and Embedding

Explores spectral theory, emphasizing regularity properties and embedding theorems in the context of Sobolev spaces and compactly supported functions.

Quantum Mechanics: Operators and Eigenvalues

Covers matrix elements, operators, paths with conditions, and time evolution in quantum mechanics.

Proof of Schmidt Theorem and Entropy Properties

Covers the proof of the Schmidt theorem and properties of von Neumann entropy, including dense coding and entanglement.

Dynamical Approaches to Spectral Theory of Operators

Covers dynamical approaches to the spectral theory of operators and solutions of differential equations.

Diagonalization of Symmetric Matrices

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

Geometric Potentials and Pressure

Introduces Banach spaces for geometric potentials and pressure analysis, emphasizing equilibrium states and pressure function analyticity.

Quantum Mechanics: Spectral Basis and Schrödinger Equation

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.

Signal Processing: Basics and Spectral Analysis

Covers the basics of signal processing, linear estimation, and digital filters.

Numerical Flow Simulation: Methods and Applications

Explores numerical methods for flow simulation, including finite element, spectral, particle, and lattice Boltzmann methods.