The Gerschgorin Circle Theorem states that every eigenvalue of a square matrix lies within at least one of a set of circles in the complex plane, which are centered at the diagonal entries of the matrix and have radii equal to the sum of the absolute values of the non-diagonal entries in the corresponding row. This theorem provides a useful method for estimating the location of eigenvalues and is especially relevant when considering how perturbations can affect these eigenvalues.
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