Computing eigenvectors from a transition matrix











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












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










1 Answer
1






active

oldest

votes

















up vote
0
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





















    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














     

    draft saved


    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2998437%2fcomputing-eigenvectors-from-a-transition-matrix%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    0
    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

























      up vote
      0
      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























        up vote
        0
        down vote










        up vote
        0
        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

        284




        284






























             

            draft saved


            draft discarded



















































             


            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2998437%2fcomputing-eigenvectors-from-a-transition-matrix%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            How do I know what Microsoft account the skydrive app is syncing to?

            Image
            up vote 4 down vote favorite 1 Some time ago, I set up skydrive for my wife on her mac. But now she wants to access the files online, I cannot remember what Microsoft account I setup and linked her skydive app to and nor can I see anything in the skydrive app settings to tell me either? How can I see the name of the Microsoft account the skydive app is currently linked to? I would like to know this for skydrive app for Mac and PC onedrive share | improve this question asked Feb 25 '13 at 4:52 Gary Barrett 260 2 5 12
            Read more

            When does type information flow backwards in C++?

            Image
            up vote 62 down vote favorite 19 I just watched Stephan T. Lavavej talk at CppCon 2018 on "Class Template Argument Deduction", where at some point he incidentally says: In C++ type information almost never flows backwards ... I had to say "almost" because there's one or two cases, possibly more but very few . Despite trying to figure out which cases he might be referring to, I couldn't come up with anything. Hence the question: In which cases the C++17 standard mandates that type information propagate backwards? c++ language-lawyer c++17 share | improve this question edited 7 hours ago scohe0
            Read more

            Grease: Live!

            Image
            A tradução deste artigo está abaixo da qualidade média aceitável. É possível que tenha sido feita por um tradutor automático ou por alguém que não conhece bem o português ou a língua original do texto. Caso queira colaborar com a Wikipédia, tente encontrar a página original e melhore este verbete conforme o guia de tradução. Grease: Live! Grease: Live!  (PRT/BRA)  Estados Unidos 2016 •   cor •   130 min. min   Direção Thomas Kail Alex Rudzinski Produção Marc Platt Adam Siegel Roteiro Allan Carr Robert Cary Warren Casey Jim Jacobs Jonathan Tolins Bronte Woodard Baseado em Grease (musical) Grease (filme) Elenco Julianne Hough Aaron Tveit Vanessa Hudgens Carlos Pena Jr. Keke Palmer Carly Rae Jepsen Kether Donohue Jordan Fisher David Del Rio Andrew Call Gênero Musical Música Tom Kitt Figurino William Ivey Long Companhia(s) produtora(s) Warner Bros. Studios Distribuição Fox Lançamento 31 de Janei
            Read more