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Direct sums - Vanderbilt University

4 MA1111: LINEAR ALGEBRA I, MICHAELMAS 2016 Thus, spans are indeed subspaces. The reason that we say a set S generates the span of S is that it turns out that the span of S is the smallest subspace of V containing S.

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Injective and surjective functions

math.vanderbilt.edu

if the image of T is an n-dimensional subspace of the (n-dimensional) vector space W. But the only full-dimensional subspace of a nite-dimensional vector space is itself, so this happens if and only if the image is all of W, namely, if T is surjective. In particular, we will say that a linear transformation between vector spaces V and

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