Spectral Theorem for Operators

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Explores symmetric linear operators, eigenvalues, and eigenvectors in functional analysis.

Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

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

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

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

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

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