Concept

Spectral radius

Related lectures (32)

Iterative Methods: Linear Systems

Covers iterative methods for solving linear systems and discusses convergence criteria and spectral radius.

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Spectral Theorem: Second

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

Matrix Diagonalization: Spectral Theorem

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

Advanced analysis II: local inversion theorem

Covers the local inversion theorem and uniqueness of solutions in a ball around a point.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Computing leading eigenvalues of the transfer operator

Explores computing the leading eigenvalue of a transfer operator beyond periodic points, focusing on mathematical settings, spectral radius estimation, and the Zaremba Conjecture.

Jacobi Method

Explains the spectral radius of a matrix and its generic definition.

Jacobi Method

Presents the spectral radius of a matrix and the Jacobi method.

Quantum Measurement Postulate

Explores the verification of PVM properties and the spectral theorem for unbounded operators in quantum mechanics.

Error and Recursion

Explores iterative error calculation and the spectral radius significance in error analysis.

Properties of the Spectrum

Explores the properties of the spectrum of an operator in L(H), including compactness and spectral radius.

Spectral Analysis: Hyperbolic Surfaces

Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.

Consensus in Networked Control Systems

Explores consensus in networked control systems, covering convergence properties, normalization of eigenvectors, and rate of convergence.

Linear Operators: Basis Transformation and Eigenvalues

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

Geometric Potentials and Pressure

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

Matrix Norms: Spectral and Frobenius

Covers matrix norms, including the spectral and Frobenius norms.

Banach Spaces and Thermodynamic Formalism

Introduces Banach spaces for maximal entropy in billiard maps, discussing spectral bounds, norms, and measure construction.

Fractal Uncertainty Principle and Spectral Gaps

Explores the Fractal Uncertainty Principle, transfer operators, spectral properties, and adapted operators.

Common Orthonormal Eigenbasis to Normal Commuting Operators

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