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Let M(n, R) be the set of real positive definite symmetric (n x n)-matrices equipped with the Euclidean norm, and let A E M(n, IR). Let L(n, R) be the set of all real non-degenerate lower-triangular (n x n)-matrices equipped with the Euclidean norm, and let L : M(n,R) L(n, R) be a (differentiable) map assigning to a positive definite symmetric matrix its lowertriangular factor in the LU-decomposition. We give an effective upper estimate for IIL'(A)II.

On a Local Lipschitz Constant of the Maps Related to $LU$-Decomposition