Journal of Generalized Lie Theory and Applications

Lie Group Methods for Eigenvalue Function

HA Nazarkandi

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Abstract

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.

Article information

Source
J. Gen. Lie Theory Appl., Volume 10, Number 1 (2016), 4 pages.

Dates
First available in Project Euclid: 3 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1486090819

Digital Object Identifier
doi:10.4172/10.4172/1736-4337.1000240

Mathematical Reviews number (MathSciNet)
MR3652752

Zentralblatt MATH identifier
06685544

Keywords
Lie group Spectral manifold Submersion Eigenvalue function Spectral function

Citation

Nazarkandi, HA. Lie Group Methods for Eigenvalue Function. J. Gen. Lie Theory Appl. 10 (2016), no. 1, 4 pages. doi:10.4172/10.4172/1736-4337.1000240. https://projecteuclid.org/euclid.jglta/1486090819


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