Linear Algebra: Unitary Operators

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

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

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

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

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

Covers eigenvalues and eigenvectors in linear algebra.

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

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

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

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