抽象矩阵的可逆性探讨

Discussion on Invertibility of Abstract Matrix

矩阵理论在高等代数中处于核心地位,较为基础的是求矩阵的逆矩阵。在n阶方阵求逆矩阵的方法基础上,介绍了抽象矩阵逆矩阵的不同求法。通过具体例题对抽象矩阵可逆性进行了归纳,得出一般抽象矩阵的逆矩阵判定。给出了利用矩阵的运算以及一元二次方程的求解公式来求几类抽象矩阵逆矩阵的方法,简化了类似抽象矩阵求逆问题的计算。

Matrix theory is at the core of higher algebra,and the basic work is to find the inverse matrix of matrix.On the basis of the method of finding the inverse matrix of n-order square matrix,this paper introduces the different methods of finding the inverse matrix of abstract matrix.Through concrete examples,this paper summarizes the reversibility of abstract matrix,and obtains the judgment of inverse matrix of general abstract matrix.The study of this paper simplifies the calculation of similar abstract matrix inversion problems.