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Brauer's Theorem

If, in the Gersgorin Circle Theorem for a given $m$,

\vert a_{jj}-a_{mm}\vert>\Lambda_j+\Lambda_m

for all $j\not=m$, then exactly one Eigenvalue of ${\hbox{\sf A}}$ lies in the Disk $\Gamma_m$.


Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1121, 1979.

© 1996-9 Eric W. Weisstein