Lectures related to Function Spaces and Hilbert Spaces

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

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Covers the definition of a scalar product on a real vector space and provides examples.

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

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

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Introduces the first step in finding an orthogonal/orthonormal base in a vector space.

Explores bases in vector spaces, including linear combinations, orthogonal bases, and basis transformations using rotation matrices.

Introduces orthogonal and orthonormal families in vector spaces with scalar products.

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

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

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

Explores the postulates of Quantum Mechanics, focusing on states, time evolution, and measurement.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Introduces vector spaces, bases, and the Hilbert space, highlighting the practical implications of defining a basis in a vector space.

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

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