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- 저자 : Changjiang Bu (검색결과 4 건)
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INVOLUTORY AND S+1-POTENCY OF LINEAR COMBINATIONS OF A TRIPOTENT MATRIX AND AN ARBITRARY MATRIX
Bu, Changjiang,Zhou, Yixin The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.1
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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Involutory and s+1-potency of linear combinations of a tripotent matrix and an arbitrary matrix
Changjiang Bu,Yixin Zhou 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
Let A_1 and A_2 be n × 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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A NOTE ON LINEAR COMBINATIONS OF AN IDEMPOTENT MATRIX AND A TRIPOTENT MATRIX
Yao, Hongmei,Sun, Yanling,Xu, Chuang,Bu, Changjiang The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
Let $A_1$ and $A_2$ be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = $c_1A_1$ + $c_2A_2$, where $c_1,\;c_2$ are nonzero complex scalars. In this paper, under an assumption of $A_1A_2$ = $A_2A_1$, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idem-potent by using the property of decomposition of a tripotent matrix, i.e. if $A_2$ is tripotent, then $A_2$ = $B_1-B_2$, where $B^2_i=B_i$, i = 1, 2 and $B_1B_2=B_2B_1=0$. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.
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A note on linear combinations of an idempotent matrix and a tripotent matrix
Hongmei Yao,Yanling Sun,CHUANG XU,CHANGJIANG BU 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
Let A1 and A2 be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = c1A1 + c2A2, where c1, c2 are nonzero complex scalars. In this paper, under an assumption of A1A2 = A2A1, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idempotent by using the property of decomposition of a tripotent matrix, i.e. if A2 is tripotent, then A2 = B1 −B2, where B2 i = Bi, i = 1, 2 and B1B2 = B2B1 = 0. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again. Let A1 and A2 be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = c1A1 + c2A2, where c1, c2 are nonzero complex scalars. In this paper, under an assumption of A1A2 = A2A1, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idempotent by using the property of decomposition of a tripotent matrix, i.e. if A2 is tripotent, then A2 = B1 −B2, where B2 i = Bi, i = 1, 2 and B1B2 = B2B1 = 0. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.
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