Abstract:

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.

Key words:  generalized cubic matrix, generalized quadratic matrix, power, inverse, linear combination