Determinantal divisor rank of an integral matrix
نویسنده
چکیده
We define the determinantal divisor rank of an integral matrix to be the number of invariant factors which equal 1. Some properties of the determinantal divisor rank are proved, which are analogous to known properties of the usual rank. These include the Frobenious inequality for the rank of a product and a relation between the rank of a submatrix of a matrix and that of its complementary submatrix in the inverse or a generalized inverse of the matrix.
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