Finding Number of Nonzero eigenvalues [closed]












-2












$begingroup$


$A$ is a $3times3$ non-zero matrix such that $A^2=0$.
To find number of non-zero eigenvalues of $A$.
How to approach? If you can suggest a good easy to understand study material that would be really helpful.






eigenvalues-eigenvectors







share|cite|improve this question











$endgroup$



closed as off-topic by Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost Jan 21 at 18:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.
















  • $begingroup$
    What have you tried? What are your thoughts? Please, help us help you by letting us know what you know and where you're stuck.
    $endgroup$
    – Arthur
    Jan 21 at 12:33












  • $begingroup$
    @Arthur I feel like det(A) = 0, as det(A^2)=0, so there is one eigen value which is equals to zero. But I'm not sure
    $endgroup$
    – user194259
    Jan 21 at 13:06










  • $begingroup$
    There is at least one eigenvalue which is equal to $0$ from that argument. And it can't be 3, since $A neq 0$. That leaves either $1$ or $2$.
    $endgroup$
    – Arthur
    Jan 21 at 13:17


















-2












$begingroup$


$A$ is a $3times3$ non-zero matrix such that $A^2=0$.
To find number of non-zero eigenvalues of $A$.
How to approach? If you can suggest a good easy to understand study material that would be really helpful.






eigenvalues-eigenvectors







share|cite|improve this question











$endgroup$



closed as off-topic by Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost Jan 21 at 18:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.
















  • $begingroup$
    What have you tried? What are your thoughts? Please, help us help you by letting us know what you know and where you're stuck.
    $endgroup$
    – Arthur
    Jan 21 at 12:33












  • $begingroup$
    @Arthur I feel like det(A) = 0, as det(A^2)=0, so there is one eigen value which is equals to zero. But I'm not sure
    $endgroup$
    – user194259
    Jan 21 at 13:06










  • $begingroup$
    There is at least one eigenvalue which is equal to $0$ from that argument. And it can't be 3, since $A neq 0$. That leaves either $1$ or $2$.
    $endgroup$
    – Arthur
    Jan 21 at 13:17
















-2












-2








-2





$begingroup$


$A$ is a $3times3$ non-zero matrix such that $A^2=0$.
To find number of non-zero eigenvalues of $A$.
How to approach? If you can suggest a good easy to understand study material that would be really helpful.






eigenvalues-eigenvectors







share|cite|improve this question











$endgroup$




$A$ is a $3times3$ non-zero matrix such that $A^2=0$.
To find number of non-zero eigenvalues of $A$.
How to approach? If you can suggest a good easy to understand study material that would be really helpful.






eigenvalues-eigenvectors




eigenvalues-eigenvectors






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 21 at 12:28









Arthur

117k7116200




117k7116200










asked Jan 21 at 12:22









user194259user194259

305




305




closed as off-topic by Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost Jan 21 at 18:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost Jan 21 at 18:07


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Adrian Keister, Shaun, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.












  • $begingroup$
    What have you tried? What are your thoughts? Please, help us help you by letting us know what you know and where you're stuck.
    $endgroup$
    – Arthur
    Jan 21 at 12:33












  • $begingroup$
    @Arthur I feel like det(A) = 0, as det(A^2)=0, so there is one eigen value which is equals to zero. But I'm not sure
    $endgroup$
    – user194259
    Jan 21 at 13:06










  • $begingroup$
    There is at least one eigenvalue which is equal to $0$ from that argument. And it can't be 3, since $A neq 0$. That leaves either $1$ or $2$.
    $endgroup$
    – Arthur
    Jan 21 at 13:17




















  • $begingroup$
    What have you tried? What are your thoughts? Please, help us help you by letting us know what you know and where you're stuck.
    $endgroup$
    – Arthur
    Jan 21 at 12:33












  • $begingroup$
    @Arthur I feel like det(A) = 0, as det(A^2)=0, so there is one eigen value which is equals to zero. But I'm not sure
    $endgroup$
    – user194259
    Jan 21 at 13:06










  • $begingroup$
    There is at least one eigenvalue which is equal to $0$ from that argument. And it can't be 3, since $A neq 0$. That leaves either $1$ or $2$.
    $endgroup$
    – Arthur
    Jan 21 at 13:17


















$begingroup$
What have you tried? What are your thoughts? Please, help us help you by letting us know what you know and where you're stuck.
$endgroup$
– Arthur
Jan 21 at 12:33






$begingroup$
What have you tried? What are your thoughts? Please, help us help you by letting us know what you know and where you're stuck.
$endgroup$
– Arthur
Jan 21 at 12:33














$begingroup$
@Arthur I feel like det(A) = 0, as det(A^2)=0, so there is one eigen value which is equals to zero. But I'm not sure
$endgroup$
– user194259
Jan 21 at 13:06




$begingroup$
@Arthur I feel like det(A) = 0, as det(A^2)=0, so there is one eigen value which is equals to zero. But I'm not sure
$endgroup$
– user194259
Jan 21 at 13:06












$begingroup$
There is at least one eigenvalue which is equal to $0$ from that argument. And it can't be 3, since $A neq 0$. That leaves either $1$ or $2$.
$endgroup$
– Arthur
Jan 21 at 13:17






$begingroup$
There is at least one eigenvalue which is equal to $0$ from that argument. And it can't be 3, since $A neq 0$. That leaves either $1$ or $2$.
$endgroup$
– Arthur
Jan 21 at 13:17












1 Answer
1






active

oldest

votes


















1












$begingroup$

Well after searching here and there I have a conclusion that A has no Nonzero eigenvalues.



AX=CX
=> (A^2)X=(C^2)X



Now A^2=0,
So C^2=0, i.e. C=0



Can anyone confirm?






share|cite|improve this answer









$endgroup$




















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    Well after searching here and there I have a conclusion that A has no Nonzero eigenvalues.



    AX=CX
    => (A^2)X=(C^2)X



    Now A^2=0,
    So C^2=0, i.e. C=0



    Can anyone confirm?






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      Well after searching here and there I have a conclusion that A has no Nonzero eigenvalues.



      AX=CX
      => (A^2)X=(C^2)X



      Now A^2=0,
      So C^2=0, i.e. C=0



      Can anyone confirm?






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        Well after searching here and there I have a conclusion that A has no Nonzero eigenvalues.



        AX=CX
        => (A^2)X=(C^2)X



        Now A^2=0,
        So C^2=0, i.e. C=0



        Can anyone confirm?






        share|cite|improve this answer









        $endgroup$



        Well after searching here and there I have a conclusion that A has no Nonzero eigenvalues.



        AX=CX
        => (A^2)X=(C^2)X



        Now A^2=0,
        So C^2=0, i.e. C=0



        Can anyone confirm?







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 21 at 13:49









        user194259user194259

        305




        305















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