![]() It is, roughly speaking, "equal" to the real line. The line y=0 is a subspace of the euclidean plane. However, knowing when a subset of a vector space is also a vector space gives you information about that particular subset. I do not think I can give you real life applications of subspaces in particular. The subspaces of these spaces all "look" different. There are vector spaces whose vectors are functions, matrices, polynomials, etc. But vector spaces are more general structures. For example, in the euclidean plane, lines that go through the origin are subspaces (can you find me more subspaces?). ![]() It must adhere to a certain list of axioms. ![]() When is a subset also a vector space? to answer this question refer to the definition of a vector space. Let W be a subset (not necessarily a subspace) of a vector space V. I will try to answer your questions in a way to try to make you develop some intuition about subspaces. ![]()
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