The Gerschgorin Circle Theorem is a mathematical result that provides a method for estimating the locations of eigenvalues of a square matrix. It states that every eigenvalue of a matrix lies within at least one Gerschgorin disk, which is centered at each diagonal element of the matrix and has a radius equal to the sum of the absolute values of the off-diagonal elements in the corresponding row. This theorem is particularly useful in numerical analysis for understanding the spectral properties of matrices used in algorithms like the QR algorithm.
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