is the identity matrix. Cayley verified this identity
and 3 and postulated that it was true for all . For , direct verification gives
The Cayley-Hamilton theorem states that an matrix is annihilated by its characteristic
which is monic of degree .
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ReferencesAyres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 181,
1962.Gradshteyn, I. S. and Ryzhik, I. M. Tables
of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
p. 1117, 2000.Segercrantz, J. "Improving the Cayley-Hamilton
Equation for Low-Rank Transformations." Amer. Math. Monthly 99,
Referenced on Wolfram|AlphaCayley-Hamilton Theorem
Cite this as:
Weisstein, Eric W. "Cayley-Hamilton Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cayley-HamiltonTheorem.html