In our course, you may have noticed that we mainly talked about orthogonally diagonalizing a matrix A E Maxn(R). What if we wanted to determine whether an arbitrary matrix A E Maxn(C) is orthogonally diagonalizable? In other words, if A € Mnxn(C), when can we find a diagonal matrix D e Maxn(C) and matrix PE Mnxn(C) such that PT = P-, for which D = P-AP? What parts of our discussion of unitary diagonalization still work, and which parts break down? Is every complex symmetric matrix orthogonally diagonalizable? Are there non-normal matrices that are orthogonally diagonalizable?

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