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    Show that a given matrix is symmetric and idempotent

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    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.

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    https://brainmass.com/math/matrices/given-matrix-symmetric-idempotent-10052

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    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.

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