An invariant of 2x2 matrices

被引：0

作者：

Cisneros-Molina, JL ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Cuernavaca 62131, Morelos, Mexico

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2005年 / 13卷

关键词：

matrix invariants; power of a matrix; trace; symmetric power of a matrix;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let W be the space of 2 x 2 matrices over a field K. Let f be any linear function on W that kills scalar matrices. Let A. W and define f(k)(A) = f(A(k)). Then the quantity f(k+ 1)(A)/f(A) is invariant under conjugation and moreover f(k+ 1)(A)/f(A) = trace S(k)A, where S(k)A is the k-th symmetric power of A, that is, the matrix giving the action of A on homogeneous polynomials of degree k.

引用

页码：146 / 152

页数：7