Lectures related to Analysis IV: Tempered Distributions and Dirac Functional

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Covers the basics of finite fields, including arithmetic operations and properties.

Covers prime numbers, vectors, 3D geometry, crystallography, and algebraic structures in materials science.

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

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Covers strategies for matrix operations and the concept of vector spaces.

Covers properties of vectorial spaces related to linear combinations and families of vectors.

Explores the definition and properties of Hermitian forms in complex vector spaces.