Lectures related to Linear Applications: Properties and Associated Matrices

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Explores changing frames in 2D through translations, rotations, and the introduction of a transformation matrix U.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explores the symmetries of the wave equation under Lorentz transformations and the Poincare group.