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# Linear Algebra : Hermitian Similar Matrices

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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.

https://brainmass.com/math/linear-algebra/linear-algebra-hermitian-similar-matrices-30855

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Hi there!
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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:

(A-wI)v=0

Where I is the identity ...

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