Lectures related to Quadratic Forms and Symmetric Bilinear Forms

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Explores symmetrical bilinear forms, the Pythagorean theorem, inequalities, and orthogonal matrices.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Explores the theory of Hermitian spaces and their applications in quadratic forms and codimension 1 spaces.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

Explores polynomial operations, properties, and subspaces in vector spaces.