Unitary similarity of the determinantal representations of unitary bordering matrices
Unitary similarity of the determinantal representations of unitary bordering matrices
复制标题
酉边界矩阵行列式表示的酉相似性
DOI：
10.1016/j.laa.2017.11.028
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发表时间：
2018
影响因子：
1.1
通讯作者：
Hiroshi Nakazato
中科院分区：
文献类型：
--
作者：
Mao-Ting Chien;Hiroshi Nakazato
令F(x,y,z)为n次双曲三元形式。 Helton–Vinnikov 定理断言存在一个 n× n 复对称矩阵 S，使得 F S (x, y, z)= F (x, y, z)，其中 n× n 矩阵 B 的行列式双曲三元形式由 F B (x, y, z)= det(x ℜ (B)+ y ℑ (B)+ z I n) 定义。设 A 为 n×n 酉边界矩阵。已知A 酉相似于对称矩阵。在本文中，我们研究了酉边界矩阵 A 和 Helton-Vinnikov 对称矩阵 S 之间的酉相似性，承认三元形式 F A (x, y, z) 的行列式表示满足 F S (x, y, z)= F A (x, y, z) 对于 n= 3, 4。
Let F (x, y, z) be a hyperbolic ternary form of degree n. The Helton–Vinnikov theorem asserts that there exists an n× n complex symmetric matrix S such that F S (x, y, z)= F (x, y, z), where the determinantal hyperbolic ternary form of an n× n matrix B is defined by F B (x, y, z)= det(x ℜ (B)+ y ℑ (B)+ z I n). Let A be an n× n unitary bordering matrix. It is known that A is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity between the unitary bordering matrix A and the Helton–Vinnikov symmetric matrix S admitted the determinantal representation of the ternary form F A (x, y, z) satisfying F S (x, y, z)= F A (x, y, z) for n= 3, 4.