2013
DOI: 10.1080/03081087.2012.689986
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On nonsingularity of combinations of three group invertible matrices and three tripotent matrices

Abstract: Let T = c1T1 + c2T2 + c3T3 − c4 (T1T2 + T3T1 + T2T3), where T1, T2, T3 are 6 three n × n tripotent matrices and c1, c2, c3, c4 are complex numbers with c1, c2, c3 7 nonzero. In this paper, it is mainly established necessary and sufficient conditions for M n be the set of all n × n complex matrices over C. The symbols rank(A), A * , R(A), 16and N (A) stands for the rank, conjugate transpose, the range space, and the null space of 17A ∈ M n , respectively. Recall that a matrix A ∈ M n is idempotent if A 2 = A an… Show more

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