Properties of Perturbative Solutions of Unilateral Matrix Equations |
| |
| Authors: | Cerchiai Bianca L. Zumino Bruno |
| |
| Affiliation: | (1) Department of Physics, University of California and Theoretical Physics Group, USA;(2) Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, 94720, U.S.A.;(3) Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, 94720, U.S.A. |
| |
| Abstract: | A left-unilateral matrix equation is an algebraic equation of the form a0+a1x+a2x2+·+anxn=0 where the coefficients ar and the unknown x are square matrices of the same order and all coefficients are on the left (similarly for a right-unilateral equation). Recently certain perturbative solutions of unilateral equations and their properties have been discussed. We present a unified approach based on the generalized Bezout theorem for matrix polynomials. Two equations discussed in the literature, their perturbative solutions and the relation between them are described. More abstractly, the coefficients and the unknown can be taken as elements of an associative, but possibly noncommutative, algebra. |
| |
| Keywords: | unilateral matrix equations |
| 本文献已被 SpringerLink 等数据库收录！ |
|
