On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation
Keyword(s):
We study the low-degree solution of the Sylvester matrix equation A 1 λ + A 0 X λ + Y λ B 1 λ + B 0 = C 0 , where A 1 λ + A 0 and B 1 λ + B 0 are regular. Using the substitution of parameter variables λ , we assume that the matrices A 0 and B 0 are invertible. Thus, we prove that if the equation is solvable, then it has a low-degree solution L λ , M λ , satisfying the degree conditions δ L λ < Ind A 0 − 1 A 1 and δ M λ < Ind B 1 B 0 − 1 .
2008 ◽
Vol 6
(3)
◽
pp. 330-332
◽
2011 ◽
Vol 9
(1)
◽
pp. 118-124
◽
Keyword(s):
2006 ◽
Vol 19
(9)
◽
pp. 859-864
◽
1996 ◽
Vol 41
(4)
◽
pp. 612-614
◽