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I need to determine the inverse of matrices of size $n \times n$. The result is only helpful if all coefficients in the inverse Matrix are strictly positive. Is there any criterion to the starting matrix?

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For starters, orthogonal matrices with positive entries. Also, check out wikipedia entry: Nonnegative_matrix. –  user2468 Jul 15 '12 at 20:20
$M$-matrices will also work. –  Cocopuffs Jul 15 '12 at 20:23
Thanks for the starting help. I am looking for an "easy to check" criterion - until now i found no criterion that makes the M-matrix check fast and uncomplicated. –  Bolek Jul 15 '12 at 20:46
You can certainly check that a matrix is Z-matrix in $n(n-1)$ comparisons. To certify that a matrix is M-matrix though one needs additional cost of computing eigenvalues (or the c/c polynomial. That's costly I admit. Bolek, what kind of matrices are looking into? Complex, real, integer? Or just general matrices? –  user2468 Jul 15 '12 at 22:59

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