Herglotz Representation Theorem

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Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Explores the matrix representation of operators and basis transformation in linear algebra.

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Explores the theory of bounded operators on Hilbert space, including adjoint properties and self-adjointness.

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Covers the criteria for operators to be self-adjoint and the Friedrichs extension theorem.

Discusses measurement in Quantum Mechanics, focusing on state vectors, observables, eigenvalues, and probabilities.