A classification of upper equivalent matrices the generic case

Abstract

Two square matricesA andB are called upper equivalent iff there exists an invertible lower triangular matrixL such thatL ⁻¹ AL andB have the same upper triangular parts. In this paper we obtain a set of invariants for this equivalence relation. In the case when any minor of a matrixA, in the intersection of its last columns and first rows and contained in its upper triangular part is different from zero, it is shown that the above mentioned set of invariants completely determines the upper triangular parts of the matrices from the equivalence class ofA. Simple representatives for this class are also given.