论文标题
有限场上的正定矩阵
Positive-Definite Matrices over Finite Fields
论文作者
论文摘要
对阳性矩阵的研究集中在Hermitian矩阵上，即具有复杂（或真实）条目的正方形矩阵，等于其自身的共轭转置。在经典环境中，正定矩阵享有许多等效的定义和属性。在本文中，我们调查了一个正方形的对称矩阵何时将来自有限领域的条目称为“正数”，并讨论哪些经典等价和含义延续了。
The study of positive-definite matrices has focused on Hermitian matrices, that is, square matrices with complex (or real) entries that are equal to their own conjugate transposes. In the classical setting, positive-definite matrices enjoy a multitude of equivalent definitions and properties. In this paper, we investigate when a square, symmetric matrix with entries coming from a finite field can be called "positive-definite" and discuss which of the classical equivalences and implications carry over.
