Function to be used for spectral decompostion of matrix

Asked Jul 08 '15 at 22:56

Active Jul 08 '15 at 23:12

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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

edited Jul 08 '15 at 23:12

J. M.'s missing motivation

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asked Jul 08 '15 at 22:56

Kausik

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. – J. M.'s missing motivation Jul 08 '15 at 23:12
Use Eigensystem and normalize the eigenvectors. – Daniel Lichtblau Jul 08 '15 at 23:49
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. – Jens Jul 09 '15 at 00:07

Function to be used for spectral decompostion of matrix

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