Eigenvalues of sum of non-symmetric matrices

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Assume $A, B$ are real matrices. Weyl's inequalities provide bounds on the eigenvalues of $A + B$ if both are symmetric. Is there any bound if neither are symmetric?



I am particularly interested about the case where $A$ and $B$ are positive stable, that is, have eigenvalues with positive real part. For instance, can one always produce $A, B$ positive stable such that $A+B$ has eigenvalues with arbitrarily negative real part?




linear-algebra matrices eigenvalues-eigenvectors




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    up vote
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    Assume $A, B$ are real matrices. Weyl's inequalities provide bounds on the eigenvalues of $A + B$ if both are symmetric. Is there any bound if neither are symmetric?



    I am particularly interested about the case where $A$ and $B$ are positive stable, that is, have eigenvalues with positive real part. For instance, can one always produce $A, B$ positive stable such that $A+B$ has eigenvalues with arbitrarily negative real part?




    linear-algebra matrices eigenvalues-eigenvectors




    share|cite|improve this question























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      Assume $A, B$ are real matrices. Weyl's inequalities provide bounds on the eigenvalues of $A + B$ if both are symmetric. Is there any bound if neither are symmetric?



      I am particularly interested about the case where $A$ and $B$ are positive stable, that is, have eigenvalues with positive real part. For instance, can one always produce $A, B$ positive stable such that $A+B$ has eigenvalues with arbitrarily negative real part?




      linear-algebra matrices eigenvalues-eigenvectors




      share|cite|improve this question













      Assume $A, B$ are real matrices. Weyl's inequalities provide bounds on the eigenvalues of $A + B$ if both are symmetric. Is there any bound if neither are symmetric?



      I am particularly interested about the case where $A$ and $B$ are positive stable, that is, have eigenvalues with positive real part. For instance, can one always produce $A, B$ positive stable such that $A+B$ has eigenvalues with arbitrarily negative real part?





      linear-algebra matrices eigenvalues-eigenvectors





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 24 at 10:53
























      asked Jul 22 at 15:36









      Nao

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