anonymous
  • anonymous
if A is a mxn matrix of rank r, what are the dim N(A) and dim N(A^T)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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nowhereman
  • nowhereman
m-r and n-r
anonymous
  • anonymous
why? I understand why dim N(A) = m-r, but is it because A is transpose that it becomes n-r?
nowhereman
  • nowhereman
yes, for the transpose the rank is the same, but it is of course a n×m-matrix then.

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anonymous
  • anonymous
thanks
anonymous
  • anonymous
actually isn't it dim N(A) = n-r and dim N(A^T) = m-r?
nowhereman
  • nowhereman
Oh yeah, mixed that up, sorry. Of course you have to subtract the rank from the domain-dimension and not from the target space dimension ^^

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