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Math Help - rank proof

  1. #1
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    rank proof

    If B and C are invertible then prove rank(BA)=rank(AC)=rank(A).
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  2. #2
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    Quote Originally Posted by hayter221 View Post
    If B and C are invertible then prove rank(BA)=rank(AC)=rank(A).
    Whether you mean matrices or linear maps is the same: as B,C are invertible they are 1-1 onto maps (matrices) so BA is an map ONTO the image of A ==> rk(BA) = rk(A), and the same with C.

    Tonio
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  3. #3
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    Hi -Based on this post, I was trying to look if there is generic rule for finding rank(AB) based on rank(A) and rank(B). I was trying to work that out but not going anywhere.

    All I could find was rank(AB)=< Min[rank(A),rank(B)]

    Can we say more?
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  4. #4
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    hey tonio, can you rephrase your response solely in terms of matrices, or would the statement be the same?
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    Quote Originally Posted by hayter221 View Post
    hey tonio, can you rephrase your response solely in terms of matrices, or would the statement be the same?

    It'd be the same using matrix language: instead of dimension of image use rank, instead of kernel use nullity, etc.

    Tonio
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