Task: Text Categorization
Input (English): Bounds for the largest coclique of an undirected, simple, loopless graph on n vertices can be found due to the interlacing of these quantities. These quantities are lowest when the Rayleigh quotient is minimized. Bounds on these quantities can be obtained using the minimax theorem of Courant and Fisher. These quantities lie in the union of closed discs in the complex plane according to a theorem of Gersgorin. Schur showed that they majorize the diagonal elements of a Hermitian matrix. If A and B are m by n and n by m complex matrices, then AB and BA have the same nonzero value for this quantity, counting multiplicity, and, as a consequence, their traces are equal. These quantities are the zeros of the characteristic polynomial. For 10 points, identify these quantities that scale an eigenvector.
Output (English): Science