Some relationships between the invariant factors of matrix and its submatrix over elementary divisor domains

Abstract

SOME RELATIONSHIPS BETWEEN THE INVARIANT FACTORS OF MATRIX AND ITS SUBMATRIX OVER ELEMENTARY DIVISOR DOMAINSRelationships between the invariant factors of matrices B and A , where B contains A as its first m rows, are investigated. In particular, we established necessary and sufficient conditions that a matrix A may be augmented with a single row to obtain a matrix B with given invariant factors over elementary divisor domains.