Abstract: | We describe all the factorizations A=BC (up to associates) of a matrix A over a commutative principal ideal domain parallel to the factorization DA=![PHgr](/content/kh287843m5276ql1/xxlarge934.gif) of its canonical diagonal form DA ( and are diagonal matrices), that is, the factorizations such that the matrices B and C are equivalent to the matrices and respectively.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 96–100. |