胡傳峰,姬秀
?
一個(gè)特殊譜任意符號(hào)模式矩陣
胡傳峰,姬秀
(長(zhǎng)江大學(xué) 文理學(xué)院,湖北 荊州 434000)
符號(hào)模式矩陣;蘊(yùn)含冪零;譜任意;極小譜任意;中心化子
符號(hào)模式矩陣主要研究其定性類中實(shí)矩陣所具有的僅與其元素符號(hào)結(jié)構(gòu)有關(guān)而與其元素?cái)?shù)值大小無(wú)關(guān)的組合性質(zhì),它起源于解決經(jīng)濟(jì)問(wèn)題,除此以外,在化學(xué)、社會(huì)學(xué)及理論計(jì)算等科學(xué)領(lǐng)域也有著極其廣泛的應(yīng)用背景.
證明 1)
因此1)成立.
引理得證.
由冪零-雅克比方法可知,實(shí)矩陣
定理得證.
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[2] BRITZ T, MCDONALD J J, OLESKY D D, et al. Minimal spectrally arbitrary sign patterns [J]. SIAM J Matrix Anal Appl, 2004, 26: 257-271.
[3] CAVERS M S, KIM I J, SHADER B L, et al. On determining minimal spectrally arbitrary patterns [J]. Elec J Linear Algebra, 2005, 13: 240-248.
[4] CAVERS M S, MEULEN K V N. Spectrally and inertially arbitrary sign patterns [J]. Linear Algebra Appl, 2005, 394: 53-72.
[5] MACGILLIVRAY G, TIFENBACH R M, DRIESSCHE van den P. Spectrally arbitrary star sign patterns [J]. Linear Algebra Appl, 2005, 400: 99-119.
[6] GARNETT C, SHADER B L. The Nilpotent-centralizer method for spectrally arbitrary sign patterns [J]. Linear Algebra Appl, 2013, 483(10): 3836-3850.
[責(zé)任編輯:熊玉濤]
A Special Spectrally Arbitrary Pattern Matrix
HUChuan-feng, JIXiu
(College of Arts and Science, Yangtze University, Jingzhou 434000, China)
sign pattern matrix; potentially Nilpotent; spectrally arbitrary sign patterns; minimal spectrally arbitrary sign patterns; centralizers
1006-7302(2014)04-0013-06
O157
A
2014-06-12
湖北省教育廳科學(xué)技術(shù)研究項(xiàng)目(B2014281);長(zhǎng)江大學(xué)文理學(xué)院科研基金資助項(xiàng)目(201303,201304)
胡傳峰(1978—),男,河南信陽(yáng)人,講師,碩士,研究方向?yàn)榻M合數(shù)學(xué)與圖論.