Clasificar el endomorfismo Tcon matriz asociada
A=
−6 8 2 −4 13 −13
10 −6−6 6 −15 17
5−6−2 3 −11 10
−1−2 4 0 −1−2
−3 3 3 −2 8 −6
8−6−4 5 −11 15
Pc(x) = (x−2)4(x2−x+ 1)
Pa(x) = (x−2)β∈{1,2,3,4}(x2−x+ 1)
dim ker (T−2I d)β= 4
(A−2Id) =
−8 8 2 −4 13 −13
10 −8−6 6 −15 17
5−6−4 3 −11 10
−1−2 4 −2−1−2
−3 3 3 −2 6 −6
8−6−4 5 −11 13
Rango (A−2Id)=4.
(A−2Id)2=
15 −15 3 3 −21 21
−15 21 3 −3 33 −27
−10 13 1 −2 20 −17
−3−3−9 0 −9 3
5−8−2 1 −13 10
−12 15 3 −3 24 −21
Rango (A−2Id)2=3.
(A−2Id)3=
−27 27 −27 0 27 −27
33 −39 27 0 −45 39
21 −24 18 0 −27 24
0 9 9 0 18 −9
−12 15 −9 0 18 −15
24 −30 18 0 −36 30
Rango (A−2Id)3=2.
ker(T−2I d)3=h(0,1,0,0,0,1),(−1,−2,0,0,1,0),(0,0,0,1,0,0),(−2,−1,1,0,0,0)i
ker(T−2I d)2=h(−2,1,1,0,0,2),(0,−3,−1,0,2,0),(−2,−1,1,4,0,0)i
e1= (0,0,0,1,0,0) ∈ker(T−2I d)3\ker(T−2I d)2
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