论文标题
Minkowski空间中的Hermitian矩阵的交织结果
An interlacing result for Hermitian matrices in Minkowski space
论文作者
论文摘要
在本文中，我们将研究一个众所周知的交织问题，但是在这里我们考虑了Minkowski空间中的Hermitian矩阵的结果，Minkowski空间是一个不确定的内部产品空间，具有一个负平方。更具体地说，我们考虑$ n \ times n $ matrix $ a = \ begin {bmatrix} j＆u \ \\ -u^*＆a \ en \ end {bmatrix} $，$ a \ in \ in \ mathbb {r {r} $，$ j = j = J =然后，相对于矩阵$ h = i_ {n-1} \ oplus（-1）$，$ a $是$ h $ selfadexhine。还讨论了配对$（a，h）$的规范形式起着重要作用，并且还讨论了与双对的标志特征。
In this paper we will look at the well known interlacing problem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the $n\times n$ matrix $A=\begin{bmatrix} J & u\\ -u^* & a\end{bmatrix}$ with $a\in\mathbb{R}$, $J=J^*$ and $u\in\mathbb{C}^{n-1}$. Then $A$ is $H$-selfadjoint with respect to the matrix $H=I_{n-1}\oplus(-1)$. The canonical form for the pair $(A,H)$ plays an important role and the sign characteristic coupled to the pair is also discussed.
