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February 11th, 2011, 06:12 AM   #1
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linear map T, finite dimensional vector space proof

if we let T: VV be a linear map, where V is a finite dimensional vector space, and suppose

Rank()=Rank()

prove that Im()=Im()
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February 11th, 2011, 09:19 AM   #2
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Re: linear map T, finite dimensional vector space proof



We know that for we have so

But the image of a linear operator is a vector space in its own right, and if vector spaces have the properties and it follows that
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