| 迹为零的对称本原矩阵的scrambling指数 |
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| 引用本文： | 张月梅,陈佘喜.迹为零的对称本原矩阵的scrambling指数[J].河南科学,2011,29(2):136-138. |
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| 作者姓名： | 张月梅 陈佘喜 |
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| 作者单位： | 湖南科技大学数学与计算科学学院,湖南湘潭,411201 |
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| 基金项目： | 湖南省科学技术厅科技计划，湖南科技大学2010年研究生创新基金资助项目 |
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| 摘 要： | 设A为n阶本原矩阵,若存在正整数k,使得对于Ak的任意两行,都在某一列上的元素为正,这样的最小正整数称为本原矩阵A的scrambling指数.采用图理论来研究对称本原A的scrambling指数.解决了迹为零的对称本原矩阵的scrambling指数的上确界问题,进而得到了其指数集,并完全刻划了这类矩阵的极矩阵.
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| 关 键 词： | 本原矩阵 scrambling指数 本原指数 有向图 |
The Scrambling Index of Zero-Trace Symmetric Primitive Matrices |
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| Zhang Yuemei,Chen Shexi.The Scrambling Index of Zero-Trace Symmetric Primitive Matrices[J].Henan Science,2011,29(2):136-138. |
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| Authors: | Zhang Yuemei Chen Shexi |
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| Institution: | (School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan 411201,Hunan China) |
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| Abstract: | The scrambing index of a primitive matrix A is the smallest positive integer k such that any two rows of Ak have at least one positive element in a coincident position.In this paper,the scrambing index of symmetric primitive matrices by using graph theory were investigated.The upper bound for the scrambing index of zero-trace symmetric primitive matrices was obtained.Moreover,the scrambing index set for this class of matrices was determined,and characterize completely the extremal matrices. |
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| Keywords: | primitive matrix scrambling index primitive exponent digraph |
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