A note on linear combinations of commuting tripotent matrices
نویسندگان
چکیده
منابع مشابه
On Nonsingularity of Linear Combinations of Tripotent Matrices
Let T1 and T2 be two commuting n × n tripotent matrices and c1, c2 two nonzero complex numbers. The problem of when a linear combination of the form T = c1T1 + c2T2 is nonsingular is considered. Some other nonsingularitytype relationships for tripotent matrices are also established. Moreover, a statistical interpretation of the results is pointed out.
متن کاملNotes on linear combinations of two tripotent , idempotent , and involutive matrices that commute
The aim of this paper is to provide alternate proofs of all the results of our previous paper [2] in the particular case when the given two matrices A1 and A2 in the linear combination A = c1A1 + c2A2 commute.
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In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.
متن کاملOn linear combinations of two commuting hypergeneralized projectors
The concept of a hypergeneralized projector as a matrix H satisfying H = H†, where H† denotes the Moore–Penrose inverse of H, was introduced by Groß and Trenkler in [Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997) 463-474]. Generalizing substantially some preliminary observations given therein, Baksalary et al. in [On some linear combinations of hypergeneralized pro...
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in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.01.011