## Mathematics, Department of

#### Date of this Version

1949

#### Abstract

We prove the following theorem.

**THEOREM 1**. Let *D* be any commutative principal ideal ring without divisors of zero, and *A* any matrix with elements in *D* whose characteristic equation factors into linear factors in *D*. Then there exists a unimodular matrix *T*, with elements in *D*, such that *T*^{-1} *AT* has zeros below the main diagonal.

## Comments

Published in

Bull. Amer. Math. Soc.55 (1949) 117-118. Used by permission.