Explore BrainMass

Explore BrainMass

    Verifying an Inner Product for Continuous Functions

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

    Please see the attached file for the fully formatted problems.

    Suppose f(x) and g(x) are continuous real-valued functions defined for [0,1]. Define vectors in &#61690;n, F= ( f(x1), f(x2), ...,f(xn)) and G= g(x1), g(x2), ...,g(xn)), where xk = k/n. Why is <F,G>n = 1/n &#61669; f(xk) g(xk) dx not an inner product for the space of continuous functions?

    © BrainMass Inc. brainmass.com March 4, 2021, 6:01 pm ad1c9bdddf
    https://brainmass.com/math/graphs-and-functions/verifying-inner-product-continuous-functions-24398

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using ...

    Solution Summary

    An inner product for continuous functions is verified. The solution is concise and well-presented.

    $2.19

    ADVERTISEMENT