Concept

Orthogonal group

Related lectures (27)

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

Orthogonality and Least Squares

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

Orthogonal Bases and Projection

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

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Orthogonal Complement in Rn

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

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Orthogonality and Projection

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

Isometries in R^n

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

Orthogonal Complement and Projection

Covers the concept of orthogonal complement and projection in vector spaces.

Orthogonal Families and Projections

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

Orthogonal Projection: Spectral Decomposition

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

Orthogonal Groups

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

Symmetric Matrices: Properties and Decomposition

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

Diagonalization of Symmetric Matrices

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

Orthogonal Families & Projections

Covers orthogonal families and projections in vector spaces, including the Gram-Schmidt process.

Aggregation queries and sorting

Covers aggregation queries and sorting of results in Geographic Information Systems.

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Orthogonality and Least Squares Methods

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

Orthogonality and Inequalities

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

Projection in Vector Spaces

Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.