Today I Learned

Some of the things I've learned every day since Oct 10, 2016

12: The Cayley-Hamilton Theorem

The Cayley-Hamilton Theorem states that a linear operator T satisfies (is annihilated by) its own characteristic polynomial.

That is, if T: V \rightarrow V is a linear operator and

f(t) = a_0 + a_1t + a_2t^2 + \dots + a_nt^n

is its characteristic polynomial, then

f(T) = a_0I + a_1T + a_2T^2 + \dots + a_nT^n = T_0,

where T_0 is the zero transformation.

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