Lecture

Vector spaces: Hilbert space

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

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

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

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

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

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

Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.

Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.

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

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

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

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

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

Explores polynomial operations, properties, and subspaces in vector spaces.

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

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

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

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

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.