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DETERMINANTS AND PERMANENTS OF POWER MATRICES

Part of: Basic linear algebra

Published online by Cambridge University Press:  17 May 2021

RATSIRI SANGUANWONG  and
KIJTI RODTES Open the ORCID record for KIJTI RODTES [Opens in a new window]
RATSIRI SANGUANWONG
Affiliation:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand e-mail: [email protected]
KIJTI RODTES*
Affiliation:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
*
e-mail: [email protected]
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Abstract

Necessary and sufficient conditions for the equality of the determinant and permanent for all powers of a given matrix are provided. The characterisation is based on a condition on merely one power.

Keywords

determinantpermanent

MSC classification

Primary: 15A15: Determinants, permanents, other special matrix functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 37 - 45
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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References

Chartrand, G., Lesniak, L. and Zhang, P., Graphs and Digraphs, 6th edn (CRC Press, Boca Raton, FL, 2016).Google Scholar
Marcus, M. and Minc, H., ‘On the relation between the determinant and the permanent’, Illinois J. Math. 5 (1961), 376–381.CrossRefGoogle Scholar
Marcus, M. and Newman, M., ‘Inequalities for the permanent function’, Ann. of Math. 75(1) (1962), 47–62.CrossRefGoogle Scholar
McCuaig, W., ‘Pólya’s permanent problem’, Electron. J. Combin. 11 (2004), R79.CrossRefGoogle Scholar
Pólya, G., ‘Aufgabe 424’, Arch. Math. Phys. 20(3) (1913), 271.Google Scholar
Szegő, G., ‘Losungzu 424’, Arch. Math. Phys. 21 (1913), 291–292.Google Scholar