Lectures related to Quadratic Forms and Hecke Operators

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Explains the Principal Axes Theorem for symmetric matrices and quadratic forms, showing the existence of orthogonal matrices for diagonalization.

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.