Oxford Linear Algebra - Direct Sum of Vector Spaces

Explore the concept of direct sum of vector subspaces in this 31-minute video lecture by University of Oxford mathematician Dr. Tom Crawford. Learn the formal mathematical definition of a direct sum and its alternative representation. Work through three fully-solved examples to understand how to determine if a given sum of vector spaces is a true direct sum. Examine the intersection of vector spaces and construct bases for subspaces to verify direct sum properties. Gain insights into related topics such as subspace tests, dimension formulas, and the sum of subspaces. Access additional resources, including practice exercises and complementary video lectures, to reinforce your understanding of linear algebra concepts.