非负矩阵级数收敛性判断

The convergence of nonnegative matrix series

为判断非负矩阵级数收敛性,通过类比非负矩阵级数与正数项级数的一些性质,证明了非负矩阵级数的M判别法、比较原则、比较判别法定理及推论.证明了可以通过布尔矩阵和函数矩阵的反常积分判别非负矩阵级数的收敛性.

For judging the convergence of the nonnegative matrix series ,by analogy properties of the non-negative matrix series and the positive terms series ,theorems and deductions of M discriminant method , comparison principle and the comparison test were proved .And it was proved that Boolean matrix and the matrix of anomalous integral could be used to judge the convergence of the series of nonnegative ma-t rix .