Computing eigenvectors from a transition matrix











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I have a 21x21 transition matrix modeling the population of a species, and I'm trying to find the long term population proportions of the states. To do this, I'm using numpy.



I found the dominant eigenvalue to be 1.128+0i, however when I access that eigenvalue's associated right eigenvector (which should give long term population proportions), I'm getting an eigenvector with complex entries.



Can a real eigenvalue have a complex eigenvector? I'm beginning to think my numpy code for calculating these values may be incorrect.



This is the matrix. Blank entries have a value of zero.






eigenvalues-eigenvectors mathematical-modeling python transition-matrix







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  • Is it possible to post the matrix?
    – Moo
    Nov 14 at 17:11










  • I edited the post.
    – FiFi
    Nov 14 at 18:02






  • 1




    Are you getting something like: $lambda =1.127649281886682$ and $v_1 = {-0.593046+0. i,-0.315548+0. i,-0.223862+0. i,-0.188595+0. i,-0.167246+0. i,-0.148314+0. i,-0.131525+0. i,-0.116637+0. i,-0.077575+0. i,-0.0233898+0. i,-0.446881+0. i,-0.237777+0. i,-0.189774+0. i,-0.159877+0. i,-0.137526+0. i,-0.118299+0. i,-0.0996625+0. i,-0.0839618+0. i,-0.0707345+0. i,-0.0439092+0. i,-0.0311509+0. i}$
    – Moo
    Nov 14 at 19:37












  • I wonder if you have some machine precision, rounding or those types of issues. Are you using infinite precision? Can you increase that?
    – Moo
    Nov 14 at 19:59










  • Ah, I figured it out. The eig() function returns the eigenvectors as columns, when I was reading them as the rows. Thanks for the help.
    – FiFi
    Nov 14 at 20:55















up vote
0
down vote

favorite












I have a 21x21 transition matrix modeling the population of a species, and I'm trying to find the long term population proportions of the states. To do this, I'm using numpy.



I found the dominant eigenvalue to be 1.128+0i, however when I access that eigenvalue's associated right eigenvector (which should give long term population proportions), I'm getting an eigenvector with complex entries.



Can a real eigenvalue have a complex eigenvector? I'm beginning to think my numpy code for calculating these values may be incorrect.



This is the matrix. Blank entries have a value of zero.






eigenvalues-eigenvectors mathematical-modeling python transition-matrix







share|cite|improve this question
























  • Is it possible to post the matrix?
    – Moo
    Nov 14 at 17:11










  • I edited the post.
    – FiFi
    Nov 14 at 18:02






  • 1




    Are you getting something like: $lambda =1.127649281886682$ and $v_1 = {-0.593046+0. i,-0.315548+0. i,-0.223862+0. i,-0.188595+0. i,-0.167246+0. i,-0.148314+0. i,-0.131525+0. i,-0.116637+0. i,-0.077575+0. i,-0.0233898+0. i,-0.446881+0. i,-0.237777+0. i,-0.189774+0. i,-0.159877+0. i,-0.137526+0. i,-0.118299+0. i,-0.0996625+0. i,-0.0839618+0. i,-0.0707345+0. i,-0.0439092+0. i,-0.0311509+0. i}$
    – Moo
    Nov 14 at 19:37












  • I wonder if you have some machine precision, rounding or those types of issues. Are you using infinite precision? Can you increase that?
    – Moo
    Nov 14 at 19:59










  • Ah, I figured it out. The eig() function returns the eigenvectors as columns, when I was reading them as the rows. Thanks for the help.
    – FiFi
    Nov 14 at 20:55













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have a 21x21 transition matrix modeling the population of a species, and I'm trying to find the long term population proportions of the states. To do this, I'm using numpy.



I found the dominant eigenvalue to be 1.128+0i, however when I access that eigenvalue's associated right eigenvector (which should give long term population proportions), I'm getting an eigenvector with complex entries.



Can a real eigenvalue have a complex eigenvector? I'm beginning to think my numpy code for calculating these values may be incorrect.



This is the matrix. Blank entries have a value of zero.






eigenvalues-eigenvectors mathematical-modeling python transition-matrix







share|cite|improve this question















I have a 21x21 transition matrix modeling the population of a species, and I'm trying to find the long term population proportions of the states. To do this, I'm using numpy.



I found the dominant eigenvalue to be 1.128+0i, however when I access that eigenvalue's associated right eigenvector (which should give long term population proportions), I'm getting an eigenvector with complex entries.



Can a real eigenvalue have a complex eigenvector? I'm beginning to think my numpy code for calculating these values may be incorrect.



This is the matrix. Blank entries have a value of zero.






eigenvalues-eigenvectors mathematical-modeling python transition-matrix




eigenvalues-eigenvectors mathematical-modeling python transition-matrix






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 14 at 18:02

























asked Nov 14 at 16:04









FiFi

284




284












  • Is it possible to post the matrix?
    – Moo
    Nov 14 at 17:11










  • I edited the post.
    – FiFi
    Nov 14 at 18:02






  • 1




    Are you getting something like: $lambda =1.127649281886682$ and $v_1 = {-0.593046+0. i,-0.315548+0. i,-0.223862+0. i,-0.188595+0. i,-0.167246+0. i,-0.148314+0. i,-0.131525+0. i,-0.116637+0. i,-0.077575+0. i,-0.0233898+0. i,-0.446881+0. i,-0.237777+0. i,-0.189774+0. i,-0.159877+0. i,-0.137526+0. i,-0.118299+0. i,-0.0996625+0. i,-0.0839618+0. i,-0.0707345+0. i,-0.0439092+0. i,-0.0311509+0. i}$
    – Moo
    Nov 14 at 19:37












  • I wonder if you have some machine precision, rounding or those types of issues. Are you using infinite precision? Can you increase that?
    – Moo
    Nov 14 at 19:59










  • Ah, I figured it out. The eig() function returns the eigenvectors as columns, when I was reading them as the rows. Thanks for the help.
    – FiFi
    Nov 14 at 20:55


















  • Is it possible to post the matrix?
    – Moo
    Nov 14 at 17:11










  • I edited the post.
    – FiFi
    Nov 14 at 18:02






  • 1




    Are you getting something like: $lambda =1.127649281886682$ and $v_1 = {-0.593046+0. i,-0.315548+0. i,-0.223862+0. i,-0.188595+0. i,-0.167246+0. i,-0.148314+0. i,-0.131525+0. i,-0.116637+0. i,-0.077575+0. i,-0.0233898+0. i,-0.446881+0. i,-0.237777+0. i,-0.189774+0. i,-0.159877+0. i,-0.137526+0. i,-0.118299+0. i,-0.0996625+0. i,-0.0839618+0. i,-0.0707345+0. i,-0.0439092+0. i,-0.0311509+0. i}$
    – Moo
    Nov 14 at 19:37












  • I wonder if you have some machine precision, rounding or those types of issues. Are you using infinite precision? Can you increase that?
    – Moo
    Nov 14 at 19:59










  • Ah, I figured it out. The eig() function returns the eigenvectors as columns, when I was reading them as the rows. Thanks for the help.
    – FiFi
    Nov 14 at 20:55
















Is it possible to post the matrix?
– Moo
Nov 14 at 17:11




Is it possible to post the matrix?
– Moo
Nov 14 at 17:11












I edited the post.
– FiFi
Nov 14 at 18:02




I edited the post.
– FiFi
Nov 14 at 18:02




1




1




Are you getting something like: $lambda =1.127649281886682$ and $v_1 = {-0.593046+0. i,-0.315548+0. i,-0.223862+0. i,-0.188595+0. i,-0.167246+0. i,-0.148314+0. i,-0.131525+0. i,-0.116637+0. i,-0.077575+0. i,-0.0233898+0. i,-0.446881+0. i,-0.237777+0. i,-0.189774+0. i,-0.159877+0. i,-0.137526+0. i,-0.118299+0. i,-0.0996625+0. i,-0.0839618+0. i,-0.0707345+0. i,-0.0439092+0. i,-0.0311509+0. i}$
– Moo
Nov 14 at 19:37






Are you getting something like: $lambda =1.127649281886682$ and $v_1 = {-0.593046+0. i,-0.315548+0. i,-0.223862+0. i,-0.188595+0. i,-0.167246+0. i,-0.148314+0. i,-0.131525+0. i,-0.116637+0. i,-0.077575+0. i,-0.0233898+0. i,-0.446881+0. i,-0.237777+0. i,-0.189774+0. i,-0.159877+0. i,-0.137526+0. i,-0.118299+0. i,-0.0996625+0. i,-0.0839618+0. i,-0.0707345+0. i,-0.0439092+0. i,-0.0311509+0. i}$
– Moo
Nov 14 at 19:37














I wonder if you have some machine precision, rounding or those types of issues. Are you using infinite precision? Can you increase that?
– Moo
Nov 14 at 19:59




I wonder if you have some machine precision, rounding or those types of issues. Are you using infinite precision? Can you increase that?
– Moo
Nov 14 at 19:59












Ah, I figured it out. The eig() function returns the eigenvectors as columns, when I was reading them as the rows. Thanks for the help.
– FiFi
Nov 14 at 20:55




Ah, I figured it out. The eig() function returns the eigenvectors as columns, when I was reading them as the rows. Thanks for the help.
– FiFi
Nov 14 at 20:55










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The eig() function returns the eigenvectors as columns. To access the one I needed, I took the transpose of the evecs array, and then called the desired eigenvector: evecsTrans[i]






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    The eig() function returns the eigenvectors as columns. To access the one I needed, I took the transpose of the evecs array, and then called the desired eigenvector: evecsTrans[i]






    share|cite|improve this answer

























      up vote
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      The eig() function returns the eigenvectors as columns. To access the one I needed, I took the transpose of the evecs array, and then called the desired eigenvector: evecsTrans[i]






      share|cite|improve this answer























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        up vote
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        down vote









        The eig() function returns the eigenvectors as columns. To access the one I needed, I took the transpose of the evecs array, and then called the desired eigenvector: evecsTrans[i]






        share|cite|improve this answer












        The eig() function returns the eigenvectors as columns. To access the one I needed, I took the transpose of the evecs array, and then called the desired eigenvector: evecsTrans[i]







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 14 at 20:58









        FiFi

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