Explore BrainMass

Explore BrainMass

    Linear Algebra : Hermitian Similar Matrices

    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!

    Suppose A & B are Hermitian matrices and AB=BA, show that A and B are simultaneously diagonalizable, ie, there exists an unitary matrix C so that both C*AC adn C*BC are diagonal.

    © BrainMass Inc. brainmass.com November 24, 2022, 11:56 am ad1c9bdddf

    Solution Preview

    Hi there!
    Thank you for posting your question to Brainmass!

    What you actually want to show is that A and B share the same eigenvectors. since B and a are hemitians, the matrix that is constructed from these eiegenvectors will diagonalize them both.

    An eigen vector is defined as:


    Where I is the identity ...

    Solution Summary

    Hermitian Similar Matrices are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.