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Simon proves that begin{aligned} lim _{xi downarrow xi _j} -frac{E_j xi )}{xi -xi _j} end{aligned}always exists and is non-zero if and only if 0 is an eigenvalue of (A+xi _j B) (with a more complicated statement if (xi _k = xi _j) for some (k ne j)).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com