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anonymous
 5 years ago
if A is a mxn matrix of rank r, what are the dim N(A) and dim N(A^T)?
anonymous
 5 years ago
if A is a mxn matrix of rank r, what are the dim N(A) and dim N(A^T)?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why? I understand why dim N(A) = mr, but is it because A is transpose that it becomes nr?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0yes, for the transpose the rank is the same, but it is of course a n×mmatrix then.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0actually isn't it dim N(A) = nr and dim N(A^T) = mr?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Oh yeah, mixed that up, sorry. Of course you have to subtract the rank from the domaindimension and not from the target space dimension ^^
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