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Math Help - Matrix Proof

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    Matrix Proof

    Determine the typical (j kth) entry in A*A^T and the typical entry in A^T * A
    Explain why it follows that if A*A^T or A^T * A is the zero matrix, then A = 0
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    Quote Originally Posted by razorfever View Post
    Determine the typical (j kth) entry in A*A^T and the typical entry in A^T * A
    Explain why it follows that if A*A^T or A^T * A is the zero matrix, then A = 0
    Since we are able to multiple  A A^t and  A^t A then A is square. If you look at the diagonal elements of say A A^t they are of the form

    A A^t_{ii} = \sum_{j=1}^n a_{i j}^2

    and since A A^t = 0 then
    \sum_{j=1}^n a_{i j}^2 = 0\;\;\Rightarrow\;\;a_{ij} = 0\;\; \forall i,j
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