Lie Group Methods for Eigenvalue FunctionNazarkandi HA*
Departement of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran
- *Corresponding Author:
- Nazarkandi HA
Departement of Mathematics
Marand Branch, Islamic Azad University
E-mail: [email protected]
Received Date: February 13, 2016; Accepted Date: June 15, 2016; Published Date: June 20, 2016
Citation: Nazarkandi HA (2016) Lie Group Methods for Eigenvalue Function. J Generalized Lie Theory Appl 10:240. doi:10.4172/10.4172/1736-4337.1000240
Copyright: © 2016 Nazarkandi HA. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.