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Cayley–Hamilton Theorem
Cayley–Hamilton Theorem
📜
The statement of the theorem
Every square matrix over a commutative ring satisfies its own characteristic equation; that is, if
p
(
λ
)
=
det
(
λ
I
−
A
)
p(\lambda) = \det(\lambda I - A)
p
(
λ
)
=
det
(
λ
I
−
A
)
is the characteristic polynomial of
A
A
A
, then
p
(
A
)
=
0
p(A) = 0
p
(
A
)
=
0
.
Source: Wikipedia