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.
| Published in | Mathematics and Computer Science (Volume 1, Issue 2) |
| DOI | 10.11648/j.mcs.20160102.11 |
| Page(s) | 21-28 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Characteristic Polynomial, Cayley-Hamilton Theorem, Skew-Symmetric Matrix, Determinant, Pfaffian
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APA Style
M. I. Krivoruchenko. (2016). Trace Identities for Skew-Symmetric Matrices. Mathematics and Computer Science, 1(2), 21-28. https://doi.org/10.11648/j.mcs.20160102.11
ACS Style
M. I. Krivoruchenko. Trace Identities for Skew-Symmetric Matrices. Math. Comput. Sci. 2016, 1(2), 21-28. doi: 10.11648/j.mcs.20160102.11
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Download@article{10.11648/j.mcs.20160102.11,
author = {M. I. Krivoruchenko},
title = {Trace Identities for Skew-Symmetric Matrices},
journal = {Mathematics and Computer Science},
volume = {1},
number = {2},
pages = {21-28},
doi = {10.11648/j.mcs.20160102.11},
url = {https://doi.org/10.11648/j.mcs.20160102.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160102.11},
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.},
year = {2016}
}
TY - JOUR T1 - Trace Identities for Skew-Symmetric Matrices AU - M. I. Krivoruchenko Y1 - 2016/06/29 PY - 2016 N1 - https://doi.org/10.11648/j.mcs.20160102.11 DO - 10.11648/j.mcs.20160102.11 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 21 EP - 28 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20160102.11 AB - 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. VL - 1 IS - 2 ER -
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