论矩阵函数中运算的一致性

在矩阵分析中，矩阵函数是通过矩阵幂级数定义的，当矩阵函数中所含的运算是加、减、乘、除4种运算时，通过矩阵幂级数计算所得的矩阵与通过矩阵4种运算（加、减、乘、逆）直接计算所得矩阵是否一致，这是要解决的中心问题．获得的主要结果是：在一定条件下，矩阵函数f（A）÷g（A）＝f（A）g（A）]-1．利用这个结果，对一些矩阵幂级数求和比用其它方法简便．事实上，在一定条件下，若求,如果收敛半径为R，r（A）＜R，则

The Operations on the Matrix Function

Matrix function is defined by matrix series of powers in matrix analysis. The main problem solved is the relationship between the matrix generated by the matrix series of powers and the matrix generated directly by matrix operations such as addition, subtraction, multiplication and inversion, if the matrix function contains operationswhich are addition, subtraction, multiplication and division. The important result is that under certain conditions. Using this result, the calculation of the sum matriX series of powers is easier than other method. In fact, if , convergence radius is R, r(A ) < R, then