A relation between the determinant and the permanent on singular matrices

作者：Antonia Duffner M; da Cruz Henrique F^*

来源：Linear Algebra and Its Applications, 2013, 438(9): 3654-3660.

DOI：10.1016/j.laa.2012.12.029

• Linear preserver problems
• Determinant
• Permanent

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 %26gt;= 3 there is no linear transformation T : M-n(F) -%26gt; M-n(F) satisfying %26lt;br%26gt;det(X) = 0 double left right arrow per(T(X)) = 0, %26lt;br%26gt;for all X is an element of M-n(F).

• 出版日期2013-5-1