There is an invertible matrix
such that
References
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Hartwig, R. E. ``Roth's Removal Rule and the Rational Canonical Form.'' Amer. Math. Monthly 103, 332-335, 1996.
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Lancaster, P. and Tismenetsky, M. The Theory of Matrices, 2nd ed. New York: Academic Press, 1985.
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New York: Blackie and Sons, 1945.