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by Guest » Wed Jan 09, 2019 6:14 pm
What is the dimension of the kernel of a linear transformation from infinite dimensional vector space to finite dimensional vector space?
May someone help me? I think the answer is infinite but i don't know how to prove this.
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by HallsofIvy » Sat Mar 30, 2019 10:33 am
Since the "image" space is finite dimensional, the subspace of vectors in the "domain" space that are mapped to nonzero vectors must be finite dimensional. That means that all other vectors in this "domain" space are mapped to the zero vector are in the kernel which must be infinite dimensional.

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