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.
出处
《北华大学学报（自然科学版）》
CAS
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)
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
row elementary operation
row-reduced echlon form
line reduced idempotent matrix
uniqueness
canonical general solution
