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Can anybody please help in finding out what is best way to do spectral decomposition (or Eigen decomposition) of the matrix. The details of Eigen decomposition can be found in attached link 1. https://en.wikipedia.org/wiki/Matrix_decomposition (refer to section for Eigen decomposition). 2. http://www.real-statistics.com/linear-algebra-matrix-topics/spectral-decomposition/

I looked into attached help link. I see three alternatives as below; Which one of below is closest to spectral decomposition please? 1 SchurDecomposition
2 JordanDecomposition 3 HessenbergDecomposition

https://reference.wolfram.com/language/guide/MatrixDecompositions.html

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  • $\begingroup$ If your matrix is normal, but has inexact entries, SchurDecomposition[] will (or can be made to) give the spectral decomposition (in itself, a deep theorem of linear algebra); otherwise, use Eigensystem[], with the caveat that it returns unnormalized eigenvectors. $\endgroup$ – J. M.'s discontentment Jul 8 '15 at 23:12
  • $\begingroup$ Use Eigensystem and normalize the eigenvectors. $\endgroup$ – Daniel Lichtblau Jul 8 '15 at 23:49
  • $\begingroup$ The construction is in my answer to the following question:Why do the eigenvectors for two similar matrixes differ by a large amount Although the title there is different, it leads to the same question as is asked here, and therefore I would call the current Q a possible duplicate. $\endgroup$ – Jens Jul 9 '15 at 0:07