Extension of Linear Transformations

Related lectures (32)

Page 2 of 4

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Explores the matrix representation of operators and basis transformation in linear algebra.

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

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

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Discusses resolving operators' closedness and injectivity in Banach spaces.

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.