Functional Calculus: Operator Definition and Properties

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Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

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

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

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

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

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

Covers the duality principle in linear algebra and its implications in mathematics.

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.