A relation between the determinant and the permanent on singular matrices

被引：1
|
作者：
Antonia Duffner, M. [1 ]
da Cruz, Henrique F. [2 ]
机构：
[1] Univ Lisbon, Fac Ciencias, P-1700016 Lisbon, Portugal
[2] Univ Beira Interior, Dept Matemat, P-6201001 Covilha, Portugal
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 09期
关键词：
Linear preserver problems; Determinant; Permanent;
D O I：
10.1016/j.laa.2012.12.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let M-n (F) be the linear space of n-square matrices with elements in F where IF is a field with at least n elements and whose characteristic is not 2. We prove that if n >= 3 there is no linear transformation T : M-n(F) -> M-n(F) satisfying det(X) = 0 double left right arrow per(T(X)) = 0, for all X is an element of M-n(F). (C) 2013 Elsevier Inc. All rights reserved.
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页码：3654 / 3660
页数：7
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