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 KiB) downloaded 65 time(s).
Maths eigenAll Companion.sm (63 KiB) downloaded 47 time(s).
Maths Polyroots_Eigen Copy.sm (128 KiB) downloaded 52 time(s).

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 KiB) downloaded 33 time(s).

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 KiB) downloaded 65 time(s).
Maths eigenAll Companion.sm (63 KiB) downloaded 47 time(s).
Maths Polyroots_Eigen Copy.sm (128 KiB) downloaded 52 time(s).

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 KiB) downloaded 34 time(s).

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 KiB) downloaded 41 time(s).