Hermitian Spaces: Theory and Applications

Explores quadratic forms, symmetric bilinear forms, and their properties.

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

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.