三个立方幂等矩阵的线性组合的相关性质

Three cubic idempotent matrices of the linear combination of the related properties

在线性代数中,矩阵是研究问题的重要工具,而研究幂等矩阵和立方幂等矩阵的线性组合在矩阵理论和统计学中具有很强的理论和实际意义,所以幂等矩阵及立方幂等矩阵线性组合的相关性质的研究成了一个比较活跃的领域.近几年相关问题引起了许多学者的关注,并且得到了许多结果.本文在前人研究的基础上给出了三个立方幂等矩阵线性组合也是立方幂等阵的一些充分必要条件.

The matrix was an important tool in the research linear of algebra issues. Idempotent matrices and the linear combination of cubic idempotent matrices was important theoretical and practical significance in matrixtheory and linear statistical. Therefore, this had became a comparative active research field. In recent years it caused many scholars＇ attention, and got a lot of results. Some necessary and sufficient conditions for linear combination of cubic idempotent matrices be also cubic idempotent matrices was given in this paper.