The applications of the bideterminant of matrix over commutative semirings
The applications of the bideterminant of matrix over commutative semirings
复制标题
矩阵二行列式在交换半环上的应用
DOI：
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发表时间：
2017
影响因子：
1.1
通讯作者：
Xueping Wang
中科院分区：
文献类型：
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作者：
Qianyu Shu;Xueping Wang
本文讨论了交换半环上矩阵的双行列式的一些应用。首先利用矩阵的双行列式定义了矩阵的麦考伊秩，给出了n × n矩阵的麦考伊秩小于n的充要条件.然后利用这些条件研究了向量的线性相关性、向量的线性无关性和矩阵的双行列式之间的关系。最后证明了广义Cramer法则对解线性方程组是有效的。
This paper discusses some applications.of the bideterminant of matrix over commutative semirings. It first uses the.bideterminant of matrix to define the McCoy rank of a matrix and gives.some necessary and sufficient conditions that the McCoy rank of an $n\times n$ matrix is less than $n$. It then uses those conditions to investigate the.relationships among linear dependence of vectors, linear independence of vectors, and the bideterminant of matrix. It.finally shows that the generalized.Cramer's rule is valid for solving the system of linear equations.