有理随机矩阵非奇异的概率(英文)  

The Probability that a Rational Random Matrix to be Nonsingular

作　　者：冯新龙[1] 帕力旦.赛力提尼亚孜 张知难[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2008年第2期174-177,181,共5页Journal of Xinjiang University(Natural Science Edition)

基　　金：Subsidized by the NSF of China (10726006);by the China Postdoctoral Science Foundation(20070421155);by the SRPHEXJ(XJEDU2007S07);by the Doctor Foundation of Xinjiang University

摘　　要：证明了随机浮点数矩阵非奇异的概率接近于1,从而表明在求具有秩亏损的有理浮点数矩阵的秩时,没有一种数值算法是有效的.In this paper, we show that the probability of a random floating number matrix is nonsingular nears 1. Thus no numerical algorithm is effective for determining the rank of a random floating number matrix, which is original rank-deficient.

关 键 词：矩阵秩 随机矩阵 LEBESGUE测度 

分 类 号：O241.82[理学—计算数学]