Explore BrainMass

Explore BrainMass

    Matrices, Reciprocals and Characteristic Vectors

    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!

    If A is nonsingular, show that the characteristic values of A^(-1) are the reciprocals of A, and that A and A^(-1) have the same characteristic vectors.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:53 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/matrices-reciprocals-characteristic-vectors-16073

    Solution Preview

    Proof. Since A is nonsingular, the determinant of A is not zero. So, zero is not an eigenvalue of A. ...

    Solution Summary

    It is shown that if A is nonsingular, that the characteristic values of A^(-1) are the reciprocals of A, and that A and A^(-1) have the same characteristic vectors.

    $2.49

    ADVERTISEMENT