A note on companion matrices

被引:82
作者
Fiedler, M [1 ]
机构
[1] Acad Sci Czech Republ, Inst Comp Sci, Prague 18207 8, Czech Republic
关键词
companion matrix; characteristic polynomial; pentadiagonal matrix; zeros of polynomials;
D O I
10.1016/S0024-3795(03)00548-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We show that the usual companion matrix of a polynomial of degree n can be factored into a product of n matrices, n - 1 of them being the identity matrix in which a 2 x 2 identity submatrix in two consecutive rows (and columns) is replaced by an appropriate 2 x 2 matrix, the remaining being the identity matrix with the last entry replaced by possibly different entry. By a certain similarity transformation, we obtain a simple new companion matrix in a penta-diagonal form. Some generalizations are also possible. (C) 2003 Elsevier Inc. All rights reserved.
引用
收藏
页码:325 / 331
页数:7
相关论文
共 5 条
[1]   CONGENIAL MATRICES [J].
BARNETT, S .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 41 (DEC) :277-298
[2]   APPLICATIONS OF COMPANION MATRIX [J].
BRAND, L .
AMERICAN MATHEMATICAL MONTHLY, 1968, 75 (02) :146-&
[3]   STRUCTURE RANKS OF MATRICES [J].
FIEDLER, M .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 179 :119-127
[4]  
Horn R. A., 1986, Matrix analysis
[5]  
Linden H, 1998, LINEAR ALGEBRA APPL, V271, P41