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Let A$A$ be a matrix. If A$A$ is "almost" equal to A^, as to say almost equal to being a selfadjoint matrix, it follows from an argument of continuity that the eigenvalues of A are "almost" real. Same argument can be made for A "almost" -A^$A^*$, it follows from an argument of continuity that the eigenvalues of $A$ are "almost" real. Same argument can be made for $A$ "almost" $-A^*$, in which case the eigenvalues are "almost" purely imaginary. Question: Is there a way of getting a quantitative estimate on the relative or absolute value of the imaginary and real parts of the eigenvalues?

Let A be a matrix. If A is "almost" equal to A^, as to say almost equal to being a selfadjoint matrix, it follows from an argument of continuity that the eigenvalues of A are "almost" real. Same argument can be made for A "almost" -A^, in which case the eigenvalues are "almost" purely imaginary. Question: Is there a way of getting a quantitative estimate on the relative or absolute value of the imaginary and real parts of the eigenvalues?

Let $A$ be a matrix. If $A$ is "almost" equal to $A^*$, it follows from an argument of continuity that the eigenvalues of $A$ are "almost" real. Same argument can be made for $A$ "almost" $-A^*$, in which case the eigenvalues are "almost" purely imaginary. Question: Is there a way of getting a quantitative estimate on the relative or absolute value of the imaginary and real parts of the eigenvalues?

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Let A be a matrix. If A is "almost" equal to A^, as to say almost equal to being a selfadjoint matrix, it follows from an argument of continuity that the eigenvalues of A are "almost" real. Same argument can be made for A "almost" -A^, in which case the eigenvalues are "almost" purely imaginary. Question: Is there a way of getting a quantitative estimate on the relative or absolute value of the imaginary and real parts of the eigenvalues?

Let A be a matrix. If A is "almost" equal to A^, as to say almost equal to being a selfadjoint matrix, it follows from an argument of continuity that the eigenvalues of A are "almost" real. Same argument can be made for A "almost" -A^, in which case the eigenvalues are "almost" purely imaginary. Question: Is there a way of getting a quantitative estimate on the relative or absolute value of the imaginary and real parts of the eigenvalues?

Let A be a matrix. If A is "almost" equal to A^, as to say almost equal to being a selfadjoint matrix, it follows from an argument of continuity that the eigenvalues of A are "almost" real. Same argument can be made for A "almost" -A^, in which case the eigenvalues are "almost" purely imaginary. Question: Is there a way of getting a quantitative estimate on the relative or absolute value of the imaginary and real parts of the eigenvalues?

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Estimate on the real and imaginary parts of eigenvalues

Let A be a matrix. If A is "almost" equal to A^, as to say almost equal to being a selfadjoint matrix, it follows from an argument of continuity that the eigenvalues of A are "almost" real. Same argument can be made for A "almost" -A^, in which case the eigenvalues are "almost" purely imaginary. Question: Is there a way of getting a quantitative estimate on the relative or absolute value of the imaginary and real parts of the eigenvalues?