Orthogonal Groups

Related lectures (25)

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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.