Abstract:

The solutions of quadratic matrix equation were discussed via the generalized Hermite matrix. The findings show that there are necessary and sufficient conditions of matrix equation XAX=A having their generalized Hermite matrix solution, and the simple expressions of the generalized Hermite matrix solution can also be obtained. Besides, the general solutions of the matrix equations  XAY=B were given.

Key words: generalized Hermite matrix, quadratic matrix equation, matrix solution, general solution