Open Access
2016 Lie Group Methods for Eigenvalue Function
HA Nazarkandi
J. Gen. Lie Theory Appl. 10(1): 1-4 (2016). DOI: 10.4172/10.4172/1736-4337.1000240


By considering a C∞ structure on the ordered non-increasing of elements of Rn, we show that it is a differentiable manifold. By using of Lie groups, we show that eigenvalue function is a submersion. This fact is used to prove some results. These results is applied to prove a few facts about spectral manifolds and spectral functions. Orthogonal matrices act on the real symmetric matrices as a Lie transformation group. This fact, also, is used to prove the results.


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HA Nazarkandi. "Lie Group Methods for Eigenvalue Function." J. Gen. Lie Theory Appl. 10 (1) 1 - 4, 2016.


Published: 2016
First available in Project Euclid: 3 February 2017

zbMATH: 06685544
MathSciNet: MR3652752
Digital Object Identifier: 10.4172/10.4172/1736-4337.1000240

Keywords: Eigenvalue function , Lie group , spectral function , Spectral manifold , submersion

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.10 • No. 1 • 2016
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