Linear Algebra: Lecture 24: structure of subspaces, TFAE thm for direct sums

here we discuss the vector space structure of the Cartesian product of vector spaces. Then, we turn to the question of when a given vector space can be written as an internal direct sum of vector spaces. When that is possible for a given set of subspaces that simply means the vector space is isomorphic to the Cartesian product of those subspaces given the natural vector addition in the Cartesian product.

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Sir, does this course include everything related to linear algebra?