Explore BrainMass

Explore BrainMass

    Show that a given matrix is symmetric and idempotent

    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!

    Let X be a txk matrix whose columns are linearly independent. Let M=I-X(X'X)^(-1)X'. Show that M is symmetric and idempotent.

    © BrainMass Inc. brainmass.com November 24, 2022, 11:37 am ad1c9bdddf


    Solution Preview

    M is symmetric if M'=M. So let's check to see if this true.

    To transpose the second part of this matrix (after the minus side), all we do is take each element in reverse order and transpose it. Let's do ...

    Solution Summary

    The solution walks the student through the problem of proving that a given matrix is symmetric and idempotent. A step-by-step solution is provided for the student.