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# Is the intersection of two linear subspaces always a linear subspace?

From Mathematics Is A Science

Jump to navigationJump to searchQuestion: Is the intersection of two linear subspaces always a linear subspace?

Answer: Yes.

Why: We know the theorem, a subset A of a vector space V is a linear subspace iff A is closed under the algebraic operations of V. But the intersection of two algebraically closed subsets is closed...

What about the union? the complement?

What if these questions are asked about groups?