Two matrices have the same eigenvalue …












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This is an testexam question and that requires true or false and some explanataion.



2 (n x n) matrices have the same eigenvalue Pi, does A - B have eigenvalue 0?






linear-algebra eigenvalues-eigenvectors







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    No. In fact, the sum of two singular matrices may not be singular.
    $endgroup$
    – Saucy O'Path
    Jan 20 at 15:03












  • $begingroup$
    @SaucyO'Path Can you elaborate on that please? It was an exam question and didn't really understand how to prove it wrong
    $endgroup$
    – Tourna
    Jan 20 at 15:08
















1












$begingroup$


This is an testexam question and that requires true or false and some explanataion.



2 (n x n) matrices have the same eigenvalue Pi, does A - B have eigenvalue 0?






linear-algebra eigenvalues-eigenvectors







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    No. In fact, the sum of two singular matrices may not be singular.
    $endgroup$
    – Saucy O'Path
    Jan 20 at 15:03












  • $begingroup$
    @SaucyO'Path Can you elaborate on that please? It was an exam question and didn't really understand how to prove it wrong
    $endgroup$
    – Tourna
    Jan 20 at 15:08














1












1








1





$begingroup$


This is an testexam question and that requires true or false and some explanataion.



2 (n x n) matrices have the same eigenvalue Pi, does A - B have eigenvalue 0?






linear-algebra eigenvalues-eigenvectors







share|cite|improve this question











$endgroup$




This is an testexam question and that requires true or false and some explanataion.



2 (n x n) matrices have the same eigenvalue Pi, does A - B have eigenvalue 0?






linear-algebra eigenvalues-eigenvectors




linear-algebra eigenvalues-eigenvectors






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 20 at 15:07







Tourna

















asked Jan 20 at 14:54









TournaTourna

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126








  • 1




    $begingroup$
    No. In fact, the sum of two singular matrices may not be singular.
    $endgroup$
    – Saucy O'Path
    Jan 20 at 15:03












  • $begingroup$
    @SaucyO'Path Can you elaborate on that please? It was an exam question and didn't really understand how to prove it wrong
    $endgroup$
    – Tourna
    Jan 20 at 15:08














  • 1




    $begingroup$
    No. In fact, the sum of two singular matrices may not be singular.
    $endgroup$
    – Saucy O'Path
    Jan 20 at 15:03












  • $begingroup$
    @SaucyO'Path Can you elaborate on that please? It was an exam question and didn't really understand how to prove it wrong
    $endgroup$
    – Tourna
    Jan 20 at 15:08








1




1




$begingroup$
No. In fact, the sum of two singular matrices may not be singular.
$endgroup$
– Saucy O'Path
Jan 20 at 15:03






$begingroup$
No. In fact, the sum of two singular matrices may not be singular.
$endgroup$
– Saucy O'Path
Jan 20 at 15:03














$begingroup$
@SaucyO'Path Can you elaborate on that please? It was an exam question and didn't really understand how to prove it wrong
$endgroup$
– Tourna
Jan 20 at 15:08




$begingroup$
@SaucyO'Path Can you elaborate on that please? It was an exam question and didn't really understand how to prove it wrong
$endgroup$
– Tourna
Jan 20 at 15:08










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$begingroup$

$$A=begin{pmatrix}
pi &0 \
0 &0
end{pmatrix},
B=begin{pmatrix}
0 &0\
0 &pi
end{pmatrix}.$$






share|cite|improve this answer









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    $begingroup$

    $$A=begin{pmatrix}
    pi &0 \
    0 &0
    end{pmatrix},
    B=begin{pmatrix}
    0 &0\
    0 &pi
    end{pmatrix}.$$






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      $$A=begin{pmatrix}
      pi &0 \
      0 &0
      end{pmatrix},
      B=begin{pmatrix}
      0 &0\
      0 &pi
      end{pmatrix}.$$






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        $$A=begin{pmatrix}
        pi &0 \
        0 &0
        end{pmatrix},
        B=begin{pmatrix}
        0 &0\
        0 &pi
        end{pmatrix}.$$






        share|cite|improve this answer









        $endgroup$



        $$A=begin{pmatrix}
        pi &0 \
        0 &0
        end{pmatrix},
        B=begin{pmatrix}
        0 &0\
        0 &pi
        end{pmatrix}.$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 20 at 15:12









        ScientificaScientifica

        6,79641335




        6,79641335






























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