I face a problem in finding the eigen vector of matrix. It generates eigen value properly but unable to find correct eigen vector.
The given a 5x5 matrix is
A=[ 0.1151 -8.571*10^{-18} 0.1638 -2.7427*10^{-17} 0.0546
-8.571*10^{-18} 0.3436 -3.2727*10^{-17} 0.2184 9.7954*10^{-18}
0.1638 -3.2727*10^{-17} 0.506 0 0.1638
-2.7427*10^{-17} 0.2184 0 0.6025 2.4242*10^{-17}
0.0546 9.7954*10^{-18} 0.1638 2.4242*10^{-17} 0.7639 ]

Using code as given in Introduction to the use of SMath Studio
Prepared by Gilberto E. Urroz, May 2010 in appendix 7 , the eigen values mat(0.0555,0.2192,0.4657,0.7266,0.8637) are correct which are compared with scilab and python but eigen vector is incorrect? All the eigen vectors do not obey orthogonality properties. How to got correct eigen vector?

Wrote

Using code as given in Introduction to the use of SMath Studio
Prepared by Gilberto E. Urroz, May 2010in appendix 7 , the eigen values mat(0.0555,0.2192,0.4657,0.7266,0.8637) are correct which are compared with scilab and python but eigen vector is incorrect? All the eigen vectors do not obey orthogonality properties. How to got correct eigen vector?

It is important to remember that an eigenvector is not a unique thing.
For a given eigenvalue, there are infinitely many eigenvectors.
Glance through these 3 documents.
Cheers ... Jean.

Maths eigenAll.sm (22 КиБ) скачан 67 раз(а).
Maths eigenAll Companion.sm (63 КиБ) скачан 48 раз(а).
Maths Polyroots_Eigen Copy.sm (128 КиБ) скачан 52 раз(а).

Wrote

How to got correct eigen vector?

Can you attach your worksheet? I will take a look, I've never used the cited program but it seems normal (via characteristic polynomial). Normally I would use Maxima for an eigenvalue problem in SS. That always worked for me, having done some comparisons (my expensive problems being coded in Matlab and Julia).

eigenvector.sm (37 КиБ) скачан 34 раз(а).

Wrote

Wrote

How to got correct eigen vector?

Can you attach your worksheet? I will take a look, I've never used the cited program but it seems normal (via characteristic polynomial). Normally I would use Maxima for an eigenvalue problem in SS. That always worked for me, having done some comparisons (my expensive problems being coded in Matlab and Julia).

Here I am attaching some portion of my the worksheet .

Wrote

Wrote

Using code as given in Introduction to the use of SMath Studio
Prepared by Gilberto E. Urroz, May 2010in appendix 7 , the eigen values mat(0.0555,0.2192,0.4657,0.7266,0.8637) are correct which are compared with scilab and python but eigen vector is incorrect? All the eigen vectors do not obey orthogonality properties. How to got correct eigen vector?

It is important to remember that an eigenvector is not a unique thing.
For a given eigenvalue, there are infinitely many eigenvectors.
Glance through these 3 documents.
Cheers ... Jean.

Maths eigenAll.sm (22 КиБ) скачан 67 раз(а).
Maths eigenAll Companion.sm (63 КиБ) скачан 48 раз(а).
Maths Polyroots_Eigen Copy.sm (128 КиБ) скачан 52 раз(а).

Your good suggestion my problems solved partially. eigen value and eigen vectors are correct but eigenvalues are not in sorted.
I have check if the matrix elements are all integers then the eigen values and hence eigenvector sorted. Here worksheet is attached.EiegenVectoreogenValues.sm (9 КиБ) скачан 34 раз(а).

Wrote

eigenvalues are not in sorted.

That is immaterial wrt the possible project suite(s).
Gilberto Urroz sorts same as Matcad.
dn_LinAlgEigenvalues(A) sorts differently, values are same.
As well dn_LinAlgEigenvectors(A) are differently sorted
with different arithmetic sign, but numerical values same.
All those codes create confusion.
Cheers ... Jean.

Maths eigenAll.sm (39 КиБ) скачан 43 раз(а).