Linear Maps and the Duality Principle in Mathematics

Related lectures (31)

Page 3 of 4

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

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Covers the Herglotz representation theorem and the construction of projection-valued measure.

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Covers the definitions and properties of dual spaces and linear operators.

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.

Discusses measurement in Quantum Mechanics, focusing on state vectors, observables, eigenvalues, and probabilities.