Complete and Orthonormal Families

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

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

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

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

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