行简化幂等矩阵与线性方程组标准通解  

Row-reduced Idempotent Matrix and the Canonical General Solution of the Linear Equations Systems

作　　者：杨忠鹏[1,2] 刘晓敏[1] 黄爱萍[1] 

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]莆田学院数学系,福建莆田351100

出　　处：《北华大学学报（自然科学版）》2013年第3期266-272,共7页Journal of Beihua University（Natural Science）

基　　金：福建省自然科学基金项目(2010J01018);福建省高校服务海西建设重点项目(2008HX03)

摘　　要：给出了行简化幂等矩阵的定义,证明了给定n阶方阵A与唯一的行简化幂等矩阵AD行等价,因此A可分解为可逆矩阵与唯一的行简化幂等矩阵的乘积.作为应用不仅指出了对给定的m×n阶矩阵A所确定的广义行简化幂等矩阵是唯一的,而且得到了非齐次线性方程组Ax=d标准通解的显示矩阵.The definition of row-reduced idempotent matrix is proposed,and we prove that the given n×n matrix A is row equivalent with the uniqueness of the row-reduced idempotent matrix AD,therefore,the matrix A can decompose into the product of an invertible matrix and an uniqueness of the row-reduced idempotent matrix.As the application of the results,it not only proves the uniqueness of generalized row-reduced idempotent matrix for given m×n matrix A which determined,but also helps to get the display matrix of the canonical general solution of the systems of nonhomogeneous linear equations Ax=d.

关 键 词：初等行变换 行简化阶梯矩阵 行简化幂等矩阵 唯一性 标准通解 

分 类 号：O151.21[理学—数学]