Linear subspace definition3/26/2023 ![]() ![]() Strictly speaking, A Subspace is a Vector Space included in another larger Vector Space. In the context of our Hilbert space, if for every sequence ( x n) in M with a limit x H, we have x M, then M is closed. If the answer to both of these questions is yes, then \(U\) is a vector space. Now we are ready to define what a subspace is. An equivalent definition for a set M to be closed in a metric space is that if ( x n) is a sequence of elements in M that is convergent, then the limit is in M (i.e. ![]()
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