Lectures related to Untitled | EPFL Graph Search

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

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

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

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

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

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.

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

Covers the theorems related to orthogonal projection and orthonormal bases.

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

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Covers the properties and applications of orthogonal matrices.

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

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

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

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

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Explains orthogonal matrices, Gram-Schmidt process, and best vector approximation in subspaces.

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

Introduces orthogonal and symmetric matrices in linear algebra with practical examples.

Delves into singular value decomposition and its applications in linear algebra.