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Math Help - Matrix Rank

  1. #1
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    Matrix Rank

    How do you show that rank A = rank A^{T} for any m x n matrix A?
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  2. #2
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    Quote Originally Posted by antman View Post
    How do you show that rank A = rank A^{T} for any m x n matrix A?
    You should know that the coloumn space and the row space of a matrix spam a vector space of the same dimension. The row space of A is equal to the coloumn space of transpose(A) and coloumn space of A is equal to the row space of transpose(A). Therefore, we see that they are the same.
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  3. #3
    Senior Member Twig's Avatar
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    hi

    I have to say, (I am studying Linear Algebra at my university now), that a lof of proofs in LinAlg. are a bit different than the proofs in calculus.
    At least they feel like it to me.

    Like here we simply stated that the columns of A are the rows of A transpose, therefore they have the same dimension.

    thanks
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