In this paper, we construct the dual-complex Gauss transformation and propose novel algorithms for LU decomposition and partial pivoting LU decomposition of dual-complex matrices. In addition, the Cholesky and \(\textrm{LDL}^H\) decompositions of dual-complex matrices are also obtained as special cases. Strict authentication is designed to cater to applications that have a zero-tolerance policy for any modifications or alterations made to the protected object. To increase the feasibility, we first propose the dual-complex matrix representation of color images and design a scheme for strict color image authentication by means of the dual-complex LU decomposition. Numerical experiments are provided to demonstrate the efficiency of the algorithm.

在本文中，我们构造了对偶复数高斯变换，并提出了对偶复数矩阵的 LU 分解和部分枢转 LU 分解的新算法。此外，还获得了对偶复数矩阵的Cholesky分解和\(\textrm{LDL}^H\)分解作为特例。严格身份验证旨在满足对受保护对象进行任何修改或变更采取零容忍政策的应用程序。为了增加可行性，我们首先提出了彩色图像的双复数矩阵表示，并通过双复数LU分解设计了严格的彩色图像认证方案。提供数值实验来证明该算法的效率。