Hilbert Space: Geometry, Bases

Related lectures (30)

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

Explores signal approximation, orthogonal bases, Fourier series, correlation, and vector geometry.

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

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

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

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.