# Show that a given matrix is symmetric and idempotent

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

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.

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:37 am ad1c9bdddfhttps://brainmass.com/math/matrices/given-matrix-symmetric-idempotent-10052

#### Solution Preview

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

M'=[I-X(X'X)^(-1)X']'

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.

$2.49