Lectures related to Orthogonal Groups

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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, quadratic forms, diagonalization, and definiteness with examples and calculations.

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

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

Explains orthogonal families, bases, and projections in vector spaces.

Covers the concept of orthogonal complement in Rn and related propositions and theorems.

Covers the theorems related to orthogonal projection and orthonormal bases.

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

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

Explores norms, orthogonality, and the Pythagorean theorem in vector spaces.

Explores integral representations, quadratic lattices, and the Hasse Principle.

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

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

Introduces vector spaces, bases, and the Hilbert space, highlighting the practical implications of defining a basis in a vector space.

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