# To solving multiparameter problems of algebra. 7. The *PG-q* factorization method and its applications

- 9 Downloads

## Abstract

The paper continues the development of rank-factorization methods for solving certain algebraic problems for multi-parameter polynomial matrices and introduces a new rank factorization of a q-parameter polynomial m × n matrix F of full row rank (called the PG-q factorization) of the form F = PG, where \(P = \prod\limits_{k = 1}^{q - 1} {\prod\limits_{i = 1}^{n_k } {\nabla _i^{(k)} } } \) is the greatest left divisor of F; Δ _{i} ^{(k)} i is a regular (q-k)-parameter polynomial matrix the characteristic polynomial of which is a primitive polynomial over the ring of polynomials in q-k-1 variables, and G is a q-parameter polynomial matrix of rank m. The PG-q algorithm is suggested, and its applications to solving some problems of algebra are presented. Bibliography: 6 titles.

## Keywords

Characteristic Polynomial Polynomial Matrix Basis Matrix Irreducible Polynomial Factorization Algorithm## Preview

Unable to display preview. Download preview PDF.

## References

- 1.V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 5,”
*Zap. Nauchn. Semin. POMI*,**309**, 144–153 (2004).MATHGoogle Scholar - 2.V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 2,”
*Zap. Nauchn. Semin. POMI*,**296**, 89–164 (2003).MATHGoogle Scholar - 3.V. N. Kublanovskaya and V. B. Khazanov, “Relative factorization of polynomials in several variables, ”
*Zh. Vychisl. Matem. Matem. Fiz.*,**36**, No. 8, 6–11 (1996).MATHMathSciNetGoogle Scholar - 4.V. B. Khazanov, “On spectral properties of multiparameter polynomial matrices,”
*Zap. Nauchn. Semin. POMI*,**229**, 184–321 (1995).Google Scholar - 5.V. N. Kublanovskaya, “An approach to solving multiparameter problems,”
*Zap. Nauchn. Semin. POMI*,**229**, 191–246 (1995).MATHGoogle Scholar - 6.V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 6,”
*Zap. Nauchn. Semin. POMI*,**323**, 132–149 (2005).MATHMathSciNetGoogle Scholar