(1)
(2)
Cayley-Hamilton Theorem
Given
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| (1) |
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| (2) |
then
| (3) |
where 
is the identity matrix. Cayley verified this identity for 
and 3 and postulated that it was true for all 
. For 
, direct verification gives
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| (4) |
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| (5) |
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| (6) |
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| (7) |
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| (8) |
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| (9) |
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| (10) |
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| (11) |
so
| (12) |
The Cayley-Hamilton theorem states that an 
matrix 
is annihilated by its characteristic polynomial 
, which is monic of degree .
