Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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INVOLUTORY AND S+1-POTENCY OF LINEAR COMBINATIONS OF A TRIPOTENT MATRIX AND AN ARBITRARY MATRIX

  • Bu, Changjiang (Department of Applied Mathematics, College of Science, Harbin Engineering University) ;
  • Zhou, Yixin (Department of Applied Mathematics, College of Science, Harbin Engineering University)
  • 투고 : 2010.03.07
  • 심사 : 2010.06.16
  • 발행 : 2011.01.30
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초록

Let $A_1$ and $A_2$ be $n{\times}n$ nonzero complex matrices, denote a linear combination of the two matrices by $A=c_1A_1+c_2A_2$, where $c_1$, $c_2$ are nonzero complex numbers. In this paper, we research the problem of the linear combinations in the general case. We give a sufficient and necessary condition for A is an involutive matrix and s+1-potent matrix, respectively, where $A_1$ is a tripotent matrix, with $A_1A_2=A_2A_1$. Then, using the results, we also give the sufficient and necessary conditions for the involutory of the linear combination A, where $A_1$ is a tripotent matrix, anti-idempotent matrix, and involutive matrix, respectively, and $A_2$ is a tripotent matrix, idempotent matrix, and involutive matrix, respectively, with $A_1A_2=A_2A_1$.

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