Concept
Operator theory
Related lectures (35)
Traces: Definition and Properties
Explores the definition and properties of traces in functional analysis, emphasizing uniqueness and linear operators.
Differentiating Vector Fields: DefinitionMOOC: Introduction to optimization on smooth manifolds: first order methods
Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.
Quantum Mechanics: Postulates and Observables
Explains the postulates of quantum mechanics and the representation of observables by operators.
Functional Calculus: Self-Adjoint Operators
Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.
Comparing Tangent Vectors: Parallel TransportMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores parallel transport along loops and covariant derivatives induced by metrics.
Quantum Physics I
Explores quantum state evolution, unitary operators, Heisenberg representation, spin precession, and observable averages.
Matrix Representation of Operators and Basis Transformation
Explores the matrix representation of operators and basis transformation in linear algebra.
Wigner Theorem; Translation Symmetry
Explores the Wigner theorem, translation symmetry, eigenstates, and wave functions in quantum physics.
Transient and Spatial Flow Instabilities
Explores transient and spatial growth in flow instabilities, dispersion relations, and necessary conditions for instability.
Image Processing I: Discrete Histogram Processing and Spatial Operators
Explores discrete histogram processing and spatial operators for image manipulation and noise reduction.