广义三次矩阵及其性质

Generalized Cubic Matrix and Its Properties

基于广义二次矩阵的性质和研究方法给出广义三次矩阵的定义,并证明了广义三次矩阵对幂、逆及线性运算封闭,且在某些条件下广义三次矩阵可表示为3个两两可交换且乘积为零的幂等矩阵的线性组合.结果表明,二次矩阵是广义三次矩阵的特例.

Based on the properties of generalized quadratic matrix and method used,the generalized cubic matrix was defined.It is proved that the generalized cubic matrix is closed for the power,the inverse and linear operation of the matrix.It is also pointed out that under some conditions,the generalized cubic matrix can be represented as the linear combination of three idempotent matrices which are commutative and the products are zero.The results show that genteralized quadratic matrix is a special case of the generalized cubic matrix.