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Homework Statement
The image of a linear transformation = columnspace of the matrix associated to the linear transformation.
More specifically though, given the transformation from Rn to Rm: from subspace X to subspace Y, the image of a linear transformation is equal to the set of vectors in X that are mapped to Y. This may or may not be equal to the all of the vectors in subspace X and subspace Y.
I was going to say, the Im(T) = all of the vectors in X that are mapped to Y, but the definition sounds a bit 'muddier', but I'm not entirely sure. Hence my post.
I usually draw a picture like this: http://thejuniverse.org/PUBLIC/LinearAlgebra/MATH-232/Unit.8/Presentation.1/Section7B/image.png to go with my definition, but I wanted to check.
I saw a reference book that said 'the image of a linear transformation f : V → W is the set of vectors the linear transformation maps to.'