关于和与积相等的矩阵对

摘要

If matrix pair (A,B) satisfies the condition A+B=AB,these two matrices have some connections.Some properties are presented,which are concerned with the rank,invertibility,eigenvalues,diagonalization and positive definite property of these two matrices.As an application of the obtained results,some new Kantorovich-type inequalities for the positive definite matrix are also derived in the end.%和与积相等的矩阵对之间有着密切的联系.从矩阵的秩、非奇异性、特征值、对角化、正定性等方面,讨论了这对矩阵的一些性质.最后,作为应用,导出了几个新的关于正定矩阵的Kantorovich型矩阵不等式.