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Concept

Hilbert space

Related lectures (31)

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

Covers the quantization of topological operators and Ising models on square lattices.

Introduces Hilbert space as a big place where quantum systems evolve with unitaries.

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

Covers the applications of Segal's Conformal Field Theory in Hilbert spaces.

Covers complete and orthonormal families in a Hilbert space, discussing unique projections and vector decomposition.

Explores the incompleteness of Cc(RN, K) and the challenges of Riemann integrability.

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

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

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

Explores thought experiments with polarisation qubits of photons and the concept of superposition in Hilbert space.

Explains the postulates of quantum mechanics, including system description, evolution, measurement, composite systems, and examples with qubits.

Covers the formulation and interpretation of mechanical effects of light.

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

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

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

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

Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Covers abstract variational problems in Hilbert spaces, focusing on boundedness, continuity, and coercivity.