保持矩阵特征值之和与积的可乘线性映射

Multiplicative linear maps that preserve sum and product of matrix characteristic value

将Hochwald的保谱条件进行了弱化,在没有保谱性条件时,得到了域上n×n矩阵代数的保持矩阵特征值之和与积的可乘线性映射,将原有的Hochwald的保谱可乘线性映射进行了推广,获得了一个新的一般性结论。

The condition of preserving the spectrum of Hochwald＇s was weakened. Without the condition of preserving the spectrum, the form of linear maps and muhiplicative maps on n × n all matrix algebra that preserve the sum and the product of matrix characteristic value were obtained. A new general conclusion is received by improving the existing Hochwald＇s conclusion.