Reference Request: Structure constants for G2












9












$begingroup$


Let $G$ be a split semisimple real Lie group in characteristic zero, and let $B=TU$ be a Borel subgroup with unipotent radical $U$ and Levi $T$. Fix an ordering on the roots $Phi^+$ of $T$ in $U$, and for each root subgroup $U_{alpha}$ of $U$, let $u_{alpha}: mathbb R rightarrow U_{alpha}$ be an isomorphism.



For all $alpha, beta in Phi^+$, there exist unique real numbers $C_{alpha,beta,i,j}$ (depending on the $u_{alpha}$ and the ordering) such that for all $x, y in mathbb R$,



$$u_{alpha}(x) u_{beta}(y) u_{alpha}(x)^{-1} = u_{beta}(y) prodlimits_{substack{i,j>0\ ialpha + j beta in Phi^+}} u_{ialpha+jbeta}(C_{alpha,beta,i,j}x^iy^j)$$



I want to work out some examples with unipotent groups of exceptional semisimple groups, and am looking for table of structure constants for the root system G2. Does anyone know a reference where an ordering on the roots is chosen and these constants are written down?






reference-request rt.representation-theory lie-groups algebraic-groups lie-algebras







share|cite|improve this question











$endgroup$








  • 3




    $begingroup$
    If you differentiate and set $x,y$ to zero, surely these expressions will be more familiar, as Lie brackets of root vectors. Then they are known in the literature, using Chevalley bases, or at least their is an algorithm to uncover them.
    $endgroup$
    – Ben McKay
    Feb 10 at 7:02






  • 1




    $begingroup$
    Some time ago I wrote a memo for myself on split-octonions and $G_2$, madore.org/~david/.misc/20140711-split-octonions.pdf — what you are looking for is the second table on page 2, right? It's easy to compute, but I don't know where you could find it in the published literature.
    $endgroup$
    – Gro-Tsen
    Feb 10 at 9:18










  • $begingroup$
    Correction: $U$ is the unipotent radical of $B$ in this formulation.
    $endgroup$
    – Jim Humphreys
    Feb 10 at 15:16
















9












$begingroup$


Let $G$ be a split semisimple real Lie group in characteristic zero, and let $B=TU$ be a Borel subgroup with unipotent radical $U$ and Levi $T$. Fix an ordering on the roots $Phi^+$ of $T$ in $U$, and for each root subgroup $U_{alpha}$ of $U$, let $u_{alpha}: mathbb R rightarrow U_{alpha}$ be an isomorphism.



For all $alpha, beta in Phi^+$, there exist unique real numbers $C_{alpha,beta,i,j}$ (depending on the $u_{alpha}$ and the ordering) such that for all $x, y in mathbb R$,



$$u_{alpha}(x) u_{beta}(y) u_{alpha}(x)^{-1} = u_{beta}(y) prodlimits_{substack{i,j>0\ ialpha + j beta in Phi^+}} u_{ialpha+jbeta}(C_{alpha,beta,i,j}x^iy^j)$$



I want to work out some examples with unipotent groups of exceptional semisimple groups, and am looking for table of structure constants for the root system G2. Does anyone know a reference where an ordering on the roots is chosen and these constants are written down?






reference-request rt.representation-theory lie-groups algebraic-groups lie-algebras







share|cite|improve this question











$endgroup$








  • 3




    $begingroup$
    If you differentiate and set $x,y$ to zero, surely these expressions will be more familiar, as Lie brackets of root vectors. Then they are known in the literature, using Chevalley bases, or at least their is an algorithm to uncover them.
    $endgroup$
    – Ben McKay
    Feb 10 at 7:02






  • 1




    $begingroup$
    Some time ago I wrote a memo for myself on split-octonions and $G_2$, madore.org/~david/.misc/20140711-split-octonions.pdf — what you are looking for is the second table on page 2, right? It's easy to compute, but I don't know where you could find it in the published literature.
    $endgroup$
    – Gro-Tsen
    Feb 10 at 9:18










  • $begingroup$
    Correction: $U$ is the unipotent radical of $B$ in this formulation.
    $endgroup$
    – Jim Humphreys
    Feb 10 at 15:16














9












9








9





$begingroup$


Let $G$ be a split semisimple real Lie group in characteristic zero, and let $B=TU$ be a Borel subgroup with unipotent radical $U$ and Levi $T$. Fix an ordering on the roots $Phi^+$ of $T$ in $U$, and for each root subgroup $U_{alpha}$ of $U$, let $u_{alpha}: mathbb R rightarrow U_{alpha}$ be an isomorphism.



For all $alpha, beta in Phi^+$, there exist unique real numbers $C_{alpha,beta,i,j}$ (depending on the $u_{alpha}$ and the ordering) such that for all $x, y in mathbb R$,



$$u_{alpha}(x) u_{beta}(y) u_{alpha}(x)^{-1} = u_{beta}(y) prodlimits_{substack{i,j>0\ ialpha + j beta in Phi^+}} u_{ialpha+jbeta}(C_{alpha,beta,i,j}x^iy^j)$$



I want to work out some examples with unipotent groups of exceptional semisimple groups, and am looking for table of structure constants for the root system G2. Does anyone know a reference where an ordering on the roots is chosen and these constants are written down?






reference-request rt.representation-theory lie-groups algebraic-groups lie-algebras







share|cite|improve this question











$endgroup$




Let $G$ be a split semisimple real Lie group in characteristic zero, and let $B=TU$ be a Borel subgroup with unipotent radical $U$ and Levi $T$. Fix an ordering on the roots $Phi^+$ of $T$ in $U$, and for each root subgroup $U_{alpha}$ of $U$, let $u_{alpha}: mathbb R rightarrow U_{alpha}$ be an isomorphism.



For all $alpha, beta in Phi^+$, there exist unique real numbers $C_{alpha,beta,i,j}$ (depending on the $u_{alpha}$ and the ordering) such that for all $x, y in mathbb R$,



$$u_{alpha}(x) u_{beta}(y) u_{alpha}(x)^{-1} = u_{beta}(y) prodlimits_{substack{i,j>0\ ialpha + j beta in Phi^+}} u_{ialpha+jbeta}(C_{alpha,beta,i,j}x^iy^j)$$



I want to work out some examples with unipotent groups of exceptional semisimple groups, and am looking for table of structure constants for the root system G2. Does anyone know a reference where an ordering on the roots is chosen and these constants are written down?






reference-request rt.representation-theory lie-groups algebraic-groups lie-algebras




reference-request rt.representation-theory lie-groups algebraic-groups lie-algebras






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Feb 10 at 15:41







D_S

















asked Feb 10 at 2:21









D_SD_S

1,801619




1,801619








  • 3




    $begingroup$
    If you differentiate and set $x,y$ to zero, surely these expressions will be more familiar, as Lie brackets of root vectors. Then they are known in the literature, using Chevalley bases, or at least their is an algorithm to uncover them.
    $endgroup$
    – Ben McKay
    Feb 10 at 7:02






  • 1




    $begingroup$
    Some time ago I wrote a memo for myself on split-octonions and $G_2$, madore.org/~david/.misc/20140711-split-octonions.pdf — what you are looking for is the second table on page 2, right? It's easy to compute, but I don't know where you could find it in the published literature.
    $endgroup$
    – Gro-Tsen
    Feb 10 at 9:18










  • $begingroup$
    Correction: $U$ is the unipotent radical of $B$ in this formulation.
    $endgroup$
    – Jim Humphreys
    Feb 10 at 15:16














  • 3




    $begingroup$
    If you differentiate and set $x,y$ to zero, surely these expressions will be more familiar, as Lie brackets of root vectors. Then they are known in the literature, using Chevalley bases, or at least their is an algorithm to uncover them.
    $endgroup$
    – Ben McKay
    Feb 10 at 7:02






  • 1




    $begingroup$
    Some time ago I wrote a memo for myself on split-octonions and $G_2$, madore.org/~david/.misc/20140711-split-octonions.pdf — what you are looking for is the second table on page 2, right? It's easy to compute, but I don't know where you could find it in the published literature.
    $endgroup$
    – Gro-Tsen
    Feb 10 at 9:18










  • $begingroup$
    Correction: $U$ is the unipotent radical of $B$ in this formulation.
    $endgroup$
    – Jim Humphreys
    Feb 10 at 15:16








3




3




$begingroup$
If you differentiate and set $x,y$ to zero, surely these expressions will be more familiar, as Lie brackets of root vectors. Then they are known in the literature, using Chevalley bases, or at least their is an algorithm to uncover them.
$endgroup$
– Ben McKay
Feb 10 at 7:02




$begingroup$
If you differentiate and set $x,y$ to zero, surely these expressions will be more familiar, as Lie brackets of root vectors. Then they are known in the literature, using Chevalley bases, or at least their is an algorithm to uncover them.
$endgroup$
– Ben McKay
Feb 10 at 7:02




1




1




$begingroup$
Some time ago I wrote a memo for myself on split-octonions and $G_2$, madore.org/~david/.misc/20140711-split-octonions.pdf — what you are looking for is the second table on page 2, right? It's easy to compute, but I don't know where you could find it in the published literature.
$endgroup$
– Gro-Tsen
Feb 10 at 9:18




$begingroup$
Some time ago I wrote a memo for myself on split-octonions and $G_2$, madore.org/~david/.misc/20140711-split-octonions.pdf — what you are looking for is the second table on page 2, right? It's easy to compute, but I don't know where you could find it in the published literature.
$endgroup$
– Gro-Tsen
Feb 10 at 9:18












$begingroup$
Correction: $U$ is the unipotent radical of $B$ in this formulation.
$endgroup$
– Jim Humphreys
Feb 10 at 15:16




$begingroup$
Correction: $U$ is the unipotent radical of $B$ in this formulation.
$endgroup$
– Jim Humphreys
Feb 10 at 15:16










3 Answers
3






active

oldest

votes


















8












$begingroup$

"Simple groups of Lie type" by R. W. Carter, a table after Section 12.4. But there only the values of $C_{alphabeta11}$ are listed. An explicit form of commutator formulas inside $U^+$ is given in Table IV of "Chevalley groups over commutative rings: I. Elementary calculations" by N. Vavilov and E. Plotkin, see the picture below.



enter image description here






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Thanks! So just to be clear $ij$ means $ialpha + j beta$, where $alpha$ is the short root, right?
    $endgroup$
    – D_S
    Feb 10 at 15:58










  • $begingroup$
    @D_S Indeed, as indicated by the presence of $3alpha+2beta$.
    $endgroup$
    – Andrei Smolensky
    Feb 10 at 16:17



















5












$begingroup$

SGA III, Expose XXIII, Section 3.4.






share|cite|improve this answer









$endgroup$









  • 2




    $begingroup$
    You can find the Réédition de SGA3 at webusers.imj-prg.fr/~patrick.polo/SGA3
    $endgroup$
    – David Roberts
    Feb 10 at 10:41





















4












$begingroup$

Probably the earliest reference is the 1956-58 Chevalley seminar, available online in typed format, which has been republished in 2005 as a typeset book edited by P. Cartier: see Chapter 21. (No special assumption about the characteristic of the field is needed.) My own later treatment of the classification of simple algebraic groups followed the same method in GTM 21 (Linear Algebraic Groups, Springer, 1975, 33.5). A similar approach was taken in SGA3, as indicated by Peter McNamara. (The later more elegant approach to the classification due to Takeuchi was worked out in Jantzen's book as well as Springer's textbook.)



Note too that the Lie algebra calculations were done in my earlier book GTM 9, first in the characteristic 0 setting: see 19.3.






share|cite|improve this answer











$endgroup$













    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: "504"
    };
    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',
    autoActivateHeartbeat: false,
    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%2fmathoverflow.net%2fquestions%2f322858%2freference-request-structure-constants-for-g2%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    8












    $begingroup$

    "Simple groups of Lie type" by R. W. Carter, a table after Section 12.4. But there only the values of $C_{alphabeta11}$ are listed. An explicit form of commutator formulas inside $U^+$ is given in Table IV of "Chevalley groups over commutative rings: I. Elementary calculations" by N. Vavilov and E. Plotkin, see the picture below.



    enter image description here






    share|cite|improve this answer











    $endgroup$













    • $begingroup$
      Thanks! So just to be clear $ij$ means $ialpha + j beta$, where $alpha$ is the short root, right?
      $endgroup$
      – D_S
      Feb 10 at 15:58










    • $begingroup$
      @D_S Indeed, as indicated by the presence of $3alpha+2beta$.
      $endgroup$
      – Andrei Smolensky
      Feb 10 at 16:17
















    8












    $begingroup$

    "Simple groups of Lie type" by R. W. Carter, a table after Section 12.4. But there only the values of $C_{alphabeta11}$ are listed. An explicit form of commutator formulas inside $U^+$ is given in Table IV of "Chevalley groups over commutative rings: I. Elementary calculations" by N. Vavilov and E. Plotkin, see the picture below.



    enter image description here






    share|cite|improve this answer











    $endgroup$













    • $begingroup$
      Thanks! So just to be clear $ij$ means $ialpha + j beta$, where $alpha$ is the short root, right?
      $endgroup$
      – D_S
      Feb 10 at 15:58










    • $begingroup$
      @D_S Indeed, as indicated by the presence of $3alpha+2beta$.
      $endgroup$
      – Andrei Smolensky
      Feb 10 at 16:17














    8












    8








    8





    $begingroup$

    "Simple groups of Lie type" by R. W. Carter, a table after Section 12.4. But there only the values of $C_{alphabeta11}$ are listed. An explicit form of commutator formulas inside $U^+$ is given in Table IV of "Chevalley groups over commutative rings: I. Elementary calculations" by N. Vavilov and E. Plotkin, see the picture below.



    enter image description here






    share|cite|improve this answer











    $endgroup$



    "Simple groups of Lie type" by R. W. Carter, a table after Section 12.4. But there only the values of $C_{alphabeta11}$ are listed. An explicit form of commutator formulas inside $U^+$ is given in Table IV of "Chevalley groups over commutative rings: I. Elementary calculations" by N. Vavilov and E. Plotkin, see the picture below.



    enter image description here







    share|cite|improve this answer














    share|cite|improve this answer



    share|cite|improve this answer








    edited Feb 10 at 15:16









    YCor

    28.2k483136




    28.2k483136










    answered Feb 10 at 10:39









    Andrei SmolenskyAndrei Smolensky

    1,2681122




    1,2681122












    • $begingroup$
      Thanks! So just to be clear $ij$ means $ialpha + j beta$, where $alpha$ is the short root, right?
      $endgroup$
      – D_S
      Feb 10 at 15:58










    • $begingroup$
      @D_S Indeed, as indicated by the presence of $3alpha+2beta$.
      $endgroup$
      – Andrei Smolensky
      Feb 10 at 16:17


















    • $begingroup$
      Thanks! So just to be clear $ij$ means $ialpha + j beta$, where $alpha$ is the short root, right?
      $endgroup$
      – D_S
      Feb 10 at 15:58










    • $begingroup$
      @D_S Indeed, as indicated by the presence of $3alpha+2beta$.
      $endgroup$
      – Andrei Smolensky
      Feb 10 at 16:17
















    $begingroup$
    Thanks! So just to be clear $ij$ means $ialpha + j beta$, where $alpha$ is the short root, right?
    $endgroup$
    – D_S
    Feb 10 at 15:58




    $begingroup$
    Thanks! So just to be clear $ij$ means $ialpha + j beta$, where $alpha$ is the short root, right?
    $endgroup$
    – D_S
    Feb 10 at 15:58












    $begingroup$
    @D_S Indeed, as indicated by the presence of $3alpha+2beta$.
    $endgroup$
    – Andrei Smolensky
    Feb 10 at 16:17




    $begingroup$
    @D_S Indeed, as indicated by the presence of $3alpha+2beta$.
    $endgroup$
    – Andrei Smolensky
    Feb 10 at 16:17











    5












    $begingroup$

    SGA III, Expose XXIII, Section 3.4.






    share|cite|improve this answer









    $endgroup$









    • 2




      $begingroup$
      You can find the Réédition de SGA3 at webusers.imj-prg.fr/~patrick.polo/SGA3
      $endgroup$
      – David Roberts
      Feb 10 at 10:41


















    5












    $begingroup$

    SGA III, Expose XXIII, Section 3.4.






    share|cite|improve this answer









    $endgroup$









    • 2




      $begingroup$
      You can find the Réédition de SGA3 at webusers.imj-prg.fr/~patrick.polo/SGA3
      $endgroup$
      – David Roberts
      Feb 10 at 10:41
















    5












    5








    5





    $begingroup$

    SGA III, Expose XXIII, Section 3.4.






    share|cite|improve this answer









    $endgroup$



    SGA III, Expose XXIII, Section 3.4.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Feb 10 at 9:54









    Peter McNamaraPeter McNamara

    5,5912754




    5,5912754








    • 2




      $begingroup$
      You can find the Réédition de SGA3 at webusers.imj-prg.fr/~patrick.polo/SGA3
      $endgroup$
      – David Roberts
      Feb 10 at 10:41
















    • 2




      $begingroup$
      You can find the Réédition de SGA3 at webusers.imj-prg.fr/~patrick.polo/SGA3
      $endgroup$
      – David Roberts
      Feb 10 at 10:41










    2




    2




    $begingroup$
    You can find the Réédition de SGA3 at webusers.imj-prg.fr/~patrick.polo/SGA3
    $endgroup$
    – David Roberts
    Feb 10 at 10:41






    $begingroup$
    You can find the Réédition de SGA3 at webusers.imj-prg.fr/~patrick.polo/SGA3
    $endgroup$
    – David Roberts
    Feb 10 at 10:41













    4












    $begingroup$

    Probably the earliest reference is the 1956-58 Chevalley seminar, available online in typed format, which has been republished in 2005 as a typeset book edited by P. Cartier: see Chapter 21. (No special assumption about the characteristic of the field is needed.) My own later treatment of the classification of simple algebraic groups followed the same method in GTM 21 (Linear Algebraic Groups, Springer, 1975, 33.5). A similar approach was taken in SGA3, as indicated by Peter McNamara. (The later more elegant approach to the classification due to Takeuchi was worked out in Jantzen's book as well as Springer's textbook.)



    Note too that the Lie algebra calculations were done in my earlier book GTM 9, first in the characteristic 0 setting: see 19.3.






    share|cite|improve this answer











    $endgroup$


















      4












      $begingroup$

      Probably the earliest reference is the 1956-58 Chevalley seminar, available online in typed format, which has been republished in 2005 as a typeset book edited by P. Cartier: see Chapter 21. (No special assumption about the characteristic of the field is needed.) My own later treatment of the classification of simple algebraic groups followed the same method in GTM 21 (Linear Algebraic Groups, Springer, 1975, 33.5). A similar approach was taken in SGA3, as indicated by Peter McNamara. (The later more elegant approach to the classification due to Takeuchi was worked out in Jantzen's book as well as Springer's textbook.)



      Note too that the Lie algebra calculations were done in my earlier book GTM 9, first in the characteristic 0 setting: see 19.3.






      share|cite|improve this answer











      $endgroup$
















        4












        4








        4





        $begingroup$

        Probably the earliest reference is the 1956-58 Chevalley seminar, available online in typed format, which has been republished in 2005 as a typeset book edited by P. Cartier: see Chapter 21. (No special assumption about the characteristic of the field is needed.) My own later treatment of the classification of simple algebraic groups followed the same method in GTM 21 (Linear Algebraic Groups, Springer, 1975, 33.5). A similar approach was taken in SGA3, as indicated by Peter McNamara. (The later more elegant approach to the classification due to Takeuchi was worked out in Jantzen's book as well as Springer's textbook.)



        Note too that the Lie algebra calculations were done in my earlier book GTM 9, first in the characteristic 0 setting: see 19.3.






        share|cite|improve this answer











        $endgroup$



        Probably the earliest reference is the 1956-58 Chevalley seminar, available online in typed format, which has been republished in 2005 as a typeset book edited by P. Cartier: see Chapter 21. (No special assumption about the characteristic of the field is needed.) My own later treatment of the classification of simple algebraic groups followed the same method in GTM 21 (Linear Algebraic Groups, Springer, 1975, 33.5). A similar approach was taken in SGA3, as indicated by Peter McNamara. (The later more elegant approach to the classification due to Takeuchi was worked out in Jantzen's book as well as Springer's textbook.)



        Note too that the Lie algebra calculations were done in my earlier book GTM 9, first in the characteristic 0 setting: see 19.3.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Feb 10 at 15:16









        YCor

        28.2k483136




        28.2k483136










        answered Feb 10 at 15:12









        Jim HumphreysJim Humphreys

        41.8k494190




        41.8k494190






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to MathOverflow!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f322858%2freference-request-structure-constants-for-g2%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

            Probability when a professor distributes a quiz and homework assignment to a class of n students.

            Image
            0 0 $begingroup$ Need help with this problem. Suppose our lazy professor collects a quiz and a homework assignment from a class of n students one day, then distributes both the quizzes and the homework assignments back to the class in a random fashion for grading. Each student receives one quiz and one homework assignment to grade. (a) What is the probability that every student receives someone else's quiz to grade, and someone else's homework to grade? (b) What is the probability that no student receives both their own quiz and their own homework assignment to grade? In this case, some students may receive their own quiz, and others may receive their own homework assignment. (c) Compute the limiting probability as n approaches infinity in each case. ...
            Read more

            Aardman Animations

            Image
            Aardman Animations, Ltd. Aardman Animations Tipo privada Atividade Animação em stop-motion , Animação em CGI Fundação 1972 Fundador(es) Peter Lord David Sproxton Sede Bristol, Inglaterra  Reino Unido Proprietário(s) Dreamworks Pessoas-chave Peter Lord David Sproxton Nick Park Divisões Aardman Features Aardman Digital Aardman Commercials Aardman Broadcast Aardman International Aardman Rights Aardman Effects Aardman 3-D Systems Aardman Nathan Love AardBoiled Website oficial aardman.com ...
            Read more

            Are they similar matrix

            Image
            0 $begingroup$ Do $begin{bmatrix} 0&i&0\0&0&1\0&0&0 end{bmatrix} $ and $begin{bmatrix} 0&0&0\-i&0&0\0&1&0 end{bmatrix} $ are similar.Is this True/false Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector share | cite | improve this question edited Dec 10 '18 at 6:38 Vasanth Kris asked Dec 10 '18 at 6:19 ...
            Read more