矩阵运算在Alice-Bob物理系统建模中应用

本文主要研究的是Alice-Bob系统建模过程中提炼出来关于矩阵运算的问题,即如何求解M和x0,使得M2=I且Mx0=-x0。对于空间变量x'和x满足(平移的)对称变换的情况,我们给出了计算M和x0的详细过程。本文的计算过程体现了线性代数中分块矩阵和相似矩阵等运算技巧在数学建模过程中起到的重要作用,说明线性代数和数学建模相辅相成,互相促进。

Under investigated in this paper is the problem of matrix operation originated from the modeling process of Alice-Bob physical system,that is,how to solve M and x0 such that M2=I and Mx 0=-x0.For the case that x'and x satisfy(shifted)parity transformation,we give the detailed process of calculating M and x0.The computational process in this paper embodies the important tole of block matrix and similar matrix in linear algebra in the process of mathematical modeling.It shows that linear algebra and mathematical modeling complement and promote each other.