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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)?

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  1. nowhereman
    • 5 years ago
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    m-r and n-r

  2. anonymous
    • 5 years ago
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    why? I understand why dim N(A) = m-r, but is it because A is transpose that it becomes n-r?

  3. nowhereman
    • 5 years ago
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    yes, for the transpose the rank is the same, but it is of course a n×m-matrix then.

  4. anonymous
    • 5 years ago
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    thanks

  5. anonymous
    • 5 years ago
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    actually isn't it dim N(A) = n-r and dim N(A^T) = m-r?

  6. nowhereman
    • 5 years ago
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    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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