Question: Let A be an n ( n real matrix, all of whose eigenvalues are real. Prove that there exist an orthogonal matrix Q and an

Let A be an n ( n real matrix, all of whose eigenvalues are real. Prove that there exist an orthogonal matrix Q and an upper triangular matrix T such that QT AQ = T. This very useful result is known as Schur's Triangularization Theorem. [Hint: Adapt the proof of the Spectral Theorem.]

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