摘要
矩阵方程是线性代数的核心组成部分,其在各个领域都有广泛应用。本文对∑AiXiBi=C这一类矩阵方程进行了研究,区别于通常的解法,利用矩阵的广义逆矩阵和分块矩阵对这一类方程进行了简化计算,通过对AXB=C和A1X1B1+A2X2B2=C进行求解,得出了其解存在条件及在特定条件下的解,并对其进行了推广,使其能更广泛的利用。
Matrix equation is the core of linear algebra and it is widely applied in various fields.This article simplified a series matrix equation of ∑AiXiBi=C,using generalized inverse matrix and the block matrix equation,which is different from the usual method.By solving the matrix equations AXB=C and A1X1B1＋A2X2B2=C,the specific conditions and the solution on such conditions come to existence.This method is also promoted to make it wided used.
关键词
广义逆矩阵
矩阵方程
分块矩阵
generai reciprocal
Matrix equation
Sub-block matrix
