Explore BrainMass

Explore BrainMass

    Matrix proof

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 December 24, 2021, 5:06 pm ad1c9bdddf

    Solution Summary

    The solution provides a proof regarding matrices.