Nazarkandi HA
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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