Functional Analysis: Banach and Hilbert Spaces

Related lectures (30)

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Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Explores the space of bandlimited functions, focusing on 1-bandlimited functions as a basis and their representation through sequences.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Covers essential concepts of vectors, norms, and their properties in linear algebra.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Explains interior points, convergence of sequences, and the dense property in real numbers.

Covers the description of states in quantum mechanics and their relation to probability, expectation values, and the Schrödinger equation.

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

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.