Title: A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications
Abstract: Abstract A square matrix A of order n is said to be tripotent if A 3 = A. In this note, we give a nine-term disjoint idempotent decomposition for the linear combination of two commutative tripotent matrices and their products. Using the decomposition, we derive some closed-form formulae for the eigenvalues, determinant, rank, trace, power, inverse and group inverse of the linear combinations. In particular, we show that the linear combinations of two commutative tripotent elements and their products can produce 39 = 19,683 tripotent elements. Keywords: idempotent matrixinvolutory matrixtripotent matrixlinear combinationdisjoint idempotent decompositioneigenvaluesdeterminantranktraceinversegroup inversequadratic formchi-square distributionAMS Subject Classifications:: 15A0915A2415A2715B57 Acknowledgements The author thanks the referee for helpful suggestions and comments.
Publication Year: 2011
Publication Date: 2011-11-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 7
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