Vector spaces: Hilbert space

Related lectures (29)

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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.