Bivariate Polynomial Matrix and Smith Form

Abstract

Matrix equivalence plays a pivotal role in multidimensional systems, which are typically represented by multivariate polynomial matrices. The Smith form of matrices is one of the important research topics in polynomial matrices. This article mainly investigates the Smith forms of several types of bivariate polynomial matrices and has successfully derived several necessary and sufficient conditions for matrix equivalence.

Keywords

• matrix equivalence
• bivariate polynomial matrix
• Smith form