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    Matrix proof

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    Prove that

    ||x^(k) - x|| <= (||T||^k)(||x^(0) - x||) and
    ||x^(k) - x|| <= (||T||^k/(1-||T||))(||x^(1)-x^(0)||),

    where T is an n x n matrix with ||T|| < 1 and

    x^(k)=Tx^(k-1)+c, k=1,2,...,

    with x^(0) arbitrary, c belonging to R^n, and x=Tx+c.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:05 pm ad1c9bdddf
    https://brainmass.com/math/matrices/matrix-proof-28224

    Solution Summary

    The solution provides a proof regarding matrices.

    $2.49

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