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Math Help - A problem of algebraic complement

  1. #1
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    A problem of algebraic complement

    Assume the matrix of order n is : A = \left(\begin{array}{ccc}a_{11}&...&a_{1n}\\...&...  &...\\a_{n1}&...&a_{nn}\end{array}\right)

    and we have: \sum_{j=1}^{n}a_{ij} = \sum_{j=1}^{n}a_{ji} = 0,i = 1,2,...,n.

    show that: all the algebraic complement(the number of algebraic complements is n^{2} ) of A are equal.
    Last edited by Xingyuan; July 9th 2009 at 10:35 PM.
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  2. #2
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    Quote Originally Posted by Xingyuan View Post
    Assume the matrix of order n is : A = \left(\begin{array}{ccc}a_{11}&...&a_{1n}\\...&...  &...\\a_{n1}&...&a_{nn}\end{array}\right)

    and we have: \sum_{j=1}^{n}a_{ij} = \sum_{j=1}^{n}a_{ji} = 0,i = 1,2,...,n.

    show that: all the algebraic complement (the number of algebraic complements is n^{2} ) of A are equal.
    ... and "algebraic complement of a matrix" means what?
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