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  1. #1
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    Linear Algebra help

    Suppose A is a m x n matrix and dim(null(A)) = d. Determine dim(null(A transpose) and justify.

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  2. #2
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    Quote Originally Posted by ishan View Post
    Suppose A is a m x n matrix and dim(null(A)) = d. Determine dim(null(A transpose) and justify.

    Thank You!
    the null space of A^T is equal to the orthogonal complement of the column space of A. we know that the dimesnion of the column space of A is equal to the rank of A, which, by the rank-nullity

    theorem, is equal to n-d. thus the dimension of the orthogonal complement of the column space of A is m-n+d. \ \Box
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