On a new identity for diagonal terms of \(2 \times 2\) matrix roots. (English) Zbl 1503.15004
Let \(M\in\mathbb{R}^{2\times 2}\) be a matrix. Under certain assumptions, the authors prove that \(M\) has an \(n\)-th root matrix \(R=(r_{ij})\) for which \(\operatorname{Re} r_{11}\operatorname{Im} r_{11}=\operatorname{Re} r_{22}\operatorname{Im} r_{22}\).
Reviewer: Jorma K. Merikoski (Tampere)
MSC:
| 15A16 | Matrix exponential and similar functions of matrices |
| 15A24 | Matrix equations and identities |
References:
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| [10] | B.-S. Tam and P.-R. Huang, Nonnegative square roots of matrices,Lin. Alg. Appl.498, 404-440 (2016). Author information Peter J. Larcombe, Department of Computing and Mathematics, College of Engineering and Technology, University of Derby, Kedleston Road, Derby DE22 1GB, U.K. E-mail:p.j.larcombe@derby.ac.uk Eric J. Fennessey, BAE Systems Surface Ships Ltd., HM Naval Base, Portsmouth PO1 3NJ, U.K. E-mail:eric.fennessey@baesystems.com Lee Rawlin, 4, Scarbrough Avenue, Skegness PE25 2SY, U.K. E-mail:leerawlin@btinternet.com James Stanton, 3, Brackley Drive, Spondon, Derby DE21 7SA, U.K. E-mail:mrstanton@hotmail.co · Zbl 1335.15042 |
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