Abstract

A matrix is said to be unitoid if it can be brought to diagonal form by a congruence transformation. We say that an algorithm is rational if it is finite and uses arithmetic operations only. There exist rational methods designed for checking the congruence of particular classes of unitoid matrices, for example, Hermitian, accretive, or dissipative matrices. We propose a rational algorithm for checking the congruence of general unitoid matrices. The algorithm is heuristic in the sense that the user is required to set values of two integral parameters, M and N. The choice of these values depends on the available a priori information about the proximity of neighboring canonical angles of the matrices being checked.

中文翻译：

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一种检验Unitoid矩阵同余的合理算法

摘要

如果矩阵可以通过同余变换变为对角线形式，则称该矩阵是 unitoid。如果一个算法是有限的并且只使用算术运算，我们就说它是有理的。存在设计用于检查特定类单位矩阵的同余性的合理方法，例如 Hermitian、增加或耗散矩阵。我们提出了一种合理的算法来检查一般单位矩阵的一致性。该算法是启发式的，因为用户需要设置两个积分参数M和N 的值。这些值的选择取决于关于被检查矩阵的相邻规范角的接近度的可用先验信息。