Oxford Linear Algebra - Subspace Test

Explore the concept of subspace testing in vector spaces through this comprehensive 36-minute video lecture by University of Oxford mathematician Dr Tom Crawford. Learn the definition of a subspace, understand trivial examples, and master the subspace test. Discover how to apply this test to determine if a given set is a subspace of a vector space. Work through three detailed examples, including proving that the x-y plane is a subspace of 3D coordinate space, demonstrating that the intersection of two subspaces is always a subspace, and showing that differentiable functions form a subspace of all functions from R to R. Access additional practice exercises, workbooks, and video lectures to reinforce your understanding of subspaces and general vector spaces. Enhance your linear algebra skills with this in-depth exploration of subspace testing, perfect for students and enthusiasts of mathematics.