| 非负交换整半环上矩阵的正/负行列式保持问题 |
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| 引用本文： | 孟丽娜,郑宝东,刘威,刘雪娇,单静.非负交换整半环上矩阵的正/负行列式保持问题[J].数学的实践与认识,2011,41(18). |
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| 作者姓名： | 孟丽娜 郑宝东 刘威 刘雪娇 单静 |
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| 作者单位： | 1. 黑龙江工程学院数学系,黑龙江哈尔滨,150050
2. 哈尔滨工业大学数学系,黑龙江哈尔滨,150001 |
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| 基金项目： | 国家自然科学基金(10871056); 黑龙江省教育厅科学技术研究项目(12511457) |
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| 摘 要： | 设R为非负交换整半环,用M_n(R)表示R上所有n×n矩阵构成的矩阵半环.令T是M_n(R)到其自身的线性变换,若T满足|T(X)|~+=|X|~+,■X∈M_n(R)(或|T(X)|~-=|X|~-,(?)X∈Mn(R)),称T为M_n(R)上保持正行列式(负行列式)的线性变换.刻画了n≥4时,M_n(R)上保持正行列式/负行列式的线性满射形式.
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| 关 键 词： | 交换半环 正行列式 负行列式 保持 |
Positive/Negative Determinant Preservers for Matrices over Nonnegative Commutative Semiring without Zero Divisors |
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| MENG Li-na,ZHENG Bao-dong,LIU Wei,LIU Xue-jiao,SHAN Jing.Positive/Negative Determinant Preservers for Matrices over Nonnegative Commutative Semiring without Zero Divisors[J].Mathematics in Practice and Theory,2011,41(18). |
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| Authors: | MENG Li-na ZHENG Bao-dong LIU Wei LIU Xue-jiao SHAN Jing |
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| Affiliation: | MENG Li-na~1,ZHENG Bao-dong~2,LIU Wei~1,LIU Xue-jiao~1,SHAN Jing~1 (1.Department of Mathematics,Heilongjiang Institute of Technology,Harbin 150050,China) (2.Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China) |
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| Abstract: | Suppose R is a nonnegative commutative semiring without zero divisors,and let M_n(R) be the matrix semiring of all n×n matrices over R.A linear transformation T from M_n(R) to itself,is said to positive determinant or negative determinant preserver if |T(X)|~+ = |X|~+ for every X∈M_n(R) or |T(X)|~-= |X|~- for every X∈M_n(R).The forms of the surjective linear transformation on M_n(R) which preserve positive determinant /negative determinant are characterized when n≥4 in this paper. |
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| Keywords: | commutative semiring positive determinant negative determinant preserve |
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