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Matrices which can be optimally scaled

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Sufficient conditions are given for a matrix to be optimally scalable in the sense of minimizing its condition number. In particular, in the case of simultaneous row- and column-scaling and subordinate to thel 1- orl -norm the minimal condition number is achieved for fully indecomposable matrices.

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Businger, P.A. Matrices which can be optimally scaled. Numer. Math. 12, 346–348 (1968).

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