友矩阵的可约性及其酉等价性质

Irreducible and the Unitary-Equivalence Properties of the Companion Matrices

研究了友矩阵的一些酉等价性质,得到了友矩阵可约性的一些条件,证明了友矩阵的数值域是一个以原点为中心的圆盘的充分必要条件是该矩阵等于幂零约当块.

In this paper, some unitary-equivalence properties of the companion matrices were studies. A criterion for a companion matrix to be reducible. It is also shown that the numerical range of a were stadel companion matrix is a circular disc centered at the origin was obtained if the matrix equalsthe （nilpotent） Jordan block.