| In 1931 Semion A. Gershgorin published an important result in linear algebra which was later called "Gershgorin's Circles Theorem ". This theorem establishes that if A is a Cnxn matrix, then its eigenvalues are in some circle with center on an element ai,i of the diagonal and with radius the sum of the absolute values of the remaining entries in the row i.In the following decades there occurred an explosion of results about eigenvalue inclusion regions of a matrix A = [a i,j] &isin Cnxn many of these results are due to Richard S. Varga who in 2004 compiled and published them in his book "Gershgorin and his Circles."In this presentation we collect and extend some of these results to partitioned matrices. We also show examples of results that are not true for partitioned matrices. |
