Lectures related to Indefinite orthogonal group

Covers the theorems related to orthogonal projection and orthonormal bases.

Covers the concept of orthogonal groups in finite-dimensional vector spaces and their special properties.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Explores the standard form of isometries in R^n and the preservation of distances.

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

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

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Explores projections on lines and symmetries in 2D space, emphasizing fixed points and symmetric matrices.

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

Covers the classical Lie algebras, focusing on calculations and dimensions.

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Explores symmetries of the wave equation, linear transformations, and solutions.

Explores orthogonal matrices, eigenvalues, and orientation-preserving transformations in linear algebra.

Covers homogeneous spaces, group actions, and separating quotient spaces in mathematics.

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

Covers the method of diagonalizing a symmetric matrix using an orthogonal matrix.

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

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

Reviews Coxeter groups, reflections, rotations, and fundamental regions in finite orthogonal transformations.