Hilbert Space: Geometry, Bases

Related lectures (30)

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Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

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

Explores cross-correlation, convolution, signal approximation, orthonormal functions, and orthogonal approximation theorem in signals and systems.

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

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Explores orthonormal bases in Hilbert spaces, discussing their properties and generation using the Gram-Schmidt method.

Covers linear algebra in Dirac notation, emphasizing the scalar product and density product in quantum computations.

Explores norm equivalence in complex functions, covering homogeneity and triangular inequality.

Covers the calculation of Fourier coefficients for periodic complex signals and the concept of a complete orthonormal system.

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.