Polynomial matrix primitive factorization over arbitrary coefficient field and related results
John Guiver, N.K. Bose · IEEE Transactions on Circuits and Systems · 1982
Morf, Levy, and Kung and Youla and Gnavi presented a primitive factorization algorithm which extracts in some sense the content of a (full rank) matrixAwith entries in the ringK[z,\omega]of bivariate polynomials over some fieldK. However, the algorithms presented in both cases specify and require the coefficient fieldKto be algebraically closed-typically the field of complex numbers. It is desirable, from theoretical and computational standpoints, to have no such restriction onK; so, for example, one could do the factorization over the real field or even the field of rational numbers, provided the coefficients start out in these fields. Here an algorithm which produces a primitive factorization over an arbitrary fieldKis presented and the use of this algorithm is illustrated by a nontrivial example. Several related results leading to a general factorization theorem are stated and proved. Scopes for applying the results in various problems of scientific and engineering interest are mentioned.