Linear Operators: Boundedness and Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

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

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