Greatest common divisors of euclidean domain matrices

Abstract

One of the Euclidean Domain is the ring of polynomials over reals . Since the notion of greatest common divisor of two matrices with polynomial entries is well-defined, in this paper the same notion is generalized to two matrices with entries from any Euclidean domain. In this genaralization, the common divisors for matrices defined as either a common left or right divisor depending on whether the two matrices have the same number of rows or have the same number of columns. In determining the greatest common divisor of two matrices with entries from an Euclidean domain, the left (or right) structure matrices is observed and analyzed using the Smith Form.

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