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This can be useful when dealing with graded matrices.
Our results are new even in the case of matrices.
These matrices are especially suitable for use with high speed computers.
Some of the results generalize known results for M -matrices, N 0 -matrices, and F 0 -matrices and for inverse M -matrices, inverse N 0 -matrices, and inverse F 0 -matrices.
The method can be applied both to square and nonsquare matrices and it is particularly suitable when the number of rows and columns of the matrices are products of many factors.
We believe that our matrices are inequivalent to the matrices used by the above authors.
The nonpolar matrices used in this study are shown to be as equally effective as the conventional matrices.
It is shown that in many cases the conditions are both necessary and sufficient for the matrices to be unitarily similar to matrices of lower orders.

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