On Permutations of Matrix Products

Hans Joachim Werner () and Ingram Olkin ()
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Hans Joachim Werner: Universität Bonn, Wirtschaftswissenschaftlicher Fachbereich, Statistische Abteilung
Ingram Olkin: Stanford University, Department of Statistics

A chapter in Statistical Inference, Econometric Analysis and Matrix Algebra, 2009, pp 359-365 from Springer

Abstract: Abstract It is well-known that trace(AB) ≥ 0 for real-symmetric nonnegative definite matrices A and B. However, trace(ABC) can be positive, zero or negative, even when C is real-symmetric nonnegative definite. The genesis of the present investigation is consideration of a product of square matrices A =A 1 A 2 …A n. Permuting the factors of A leads to a different matrix product. We are interested in conditions under which the spectrum remains invariant. The main results are for square matrices over an arbitrary algebraically closed commutative field. The special case of real-symmetric, possibly nonnegative definite, matrices is also considered.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2121-5_25

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DOI: 10.1007/978-3-7908-2121-5_25

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