Functional Analysis I: Spectral Theorem

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Page 3 of 4

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

Discusses resolving operators' closedness and injectivity in Banach spaces.

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

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

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

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

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

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

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