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![]() ![]() In fact, the column space and nullspace are intricately connected by the rank-nullity theorem, which in turn is part of the fundamental theorem of linear algebra. ![]() This establishes that the nullspace is a vector space as well. As we discussed in Section 2.6, a subspace is the same as a span, except we do not have a set of spanning vectors in mind. For instance, consider the set \(W\) of complex vectors \(\mathbf \in N\) for any scalar \(c\). The sum of two subspaces U, V of W is the set, denoted. ![]() The simplest way to generate a subspace is to restrict a given vector space by some rule. But the set of all these simple sums is a subspace: Definition/Lemma. ![]()
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