martes, 26 de mayo de 2020

matrius canóniques

matriu:
(-a)     (a/2)  (-a)
(a/2)   (a/2)  (a/2)
(a/2)   (-a)    (a/2)


polinomi característic:
P(x) = (-1)·(x+a)·(-1)·(x+(-1)(a/2))·(-1)·(x+(-1)(a/2))+...
... (-1)·(-1)·(-a)·(a/2)·(x+a)+(-1)·(-1)·(-a)·(a/2)·(x+(-1)(a/2))+(-1)·(-1)·(a/2)·(a/2)·(x+(-1)(a/2))+...
... (a^{3}/8)+(a^{3}/2)


valor propi:
e^{(1/3)·pi·i}·a·(1/4)^{(1/3)}


ker de base canónica
( (-a)+(-1)·e^{(1/3)·pi·i}·a·(1/4)^{(1/3)} )·x+(a/2)·y+(-a)·z = 0
(a/2)·x+( (a/2)+(-1)·e^{(1/3)·pi·i}·a·(1/4)^{(1/3)} )·y+(a/2)·z = 0
(a/2)·x+(-a)·y+( (a/2)+(-1)·e^{(1/3)·pi·i}·a·(1/4)^{(1/3)} )·z = 0

No hay comentarios:

Publicar un comentario