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Related lectures (24)

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Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Linear Algebra: Unitary Operators

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

Explores the Sturm-Liouville eigenvalue problem, emphasizing the essential role of boundary conditions in ensuring self-adjointness and forming an orthogonal basis.

Spectral Theorem for Operators

Explores the spectral theorem for operators in a Hilbert space.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.

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Spectral Theorem: Eigenvalues and Eigenvectors

Covers the spectral theorem, eigenvalues, eigenvectors, and their importance in linear algebra.

Quantum Mechanics: Postulates and Observables

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

Homotopy Theory in Care Complexes

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Fractal Uncertainty Principle and Spectral Gaps

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