Concept

Linear subspace

Related lectures (23)

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Explores polynomial operations, properties, and subspaces in vector spaces.

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Covers the properties and criteria of linear dependence and independence in a vector space.

Explains orthogonal projection on a vector subspace in Euclidean space.

Explores vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

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

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

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

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Explains linear independence, basis, and matrix rank with examples and exercises.

Introduces linear combinations of vectors in R^n and their properties.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explores linear dependence and independence of vectors, including subspaces generation and corollaries.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.