Functional Analysis I

Related lectures (29)

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

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

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

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

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

Explores spectral and singular value decompositions of matrices.

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.

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