Trace Identities for Skew-Symmetric Matrices
Mathematics and Computer Science
Volume 1, Issue 2, July 2016, Pages: 21-28
Received: May 10, 2016; Accepted: Jun. 14, 2016; Published: Jun. 29, 2016
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Author
M. I. Krivoruchenko, Theoretical Physics Division, Institute for Theoretical and Experimental Physics, Moscow, Russia; Department of Nano/Bio, Information and Cognitive Technologies, Moscow Institute of Physics and Technology, Dolgoprudny, Russia; Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia
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Abstract
We derive an expression for the product of the Pfaffians of two skew-symmetric matrices A and B as a sum of products of the traces of powers of AB and an expression for the inverse matrix A-1, or equivalently B-1, as a finite-order polynomial of AB with coefficients depending on the traces of powers of AB.
Keywords
Characteristic Polynomial, Cayley-Hamilton Theorem, Skew-Symmetric Matrix, Determinant, Pfaffian
To cite this article
M. I. Krivoruchenko, Trace Identities for Skew-Symmetric Matrices, Mathematics and Computer Science. Vol. 1, No. 2, 2016, pp. 21-28. doi: 10.11648/j.mcs.20160102.11
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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