àlgebra lineal

A_{ij} = ( <a,d,b>,<d,a,0>,<b,0,a> )

det[A_{ij}+(-x)·Id_{33}] = (a+(-x))( (a+(-x))^{2}+(-1)·(b^{2}+d^{2}) ) = 0

( X_{ij} )^{o(-1)} o A_{ij} o X_{ij} = ...

... < a+( b^{2}+d^{2} )^{(1/2)},0,0 >,< 0,a,0 >,< 0,0,a+(-1)·( b^{2}+d^{2} )^{(1/2)} >

( A_{ij}+(-1)·x_{k}·Id_{33} ) o X_{ik} = 0_{i}

X_{i1} = < ( b^{2}+d^{2} )^{(1/2)},(-d),(-b) >

X_{i2} = < 0,b,(-d) >

X_{i3} = < ( b^{2}+d^{2} )^{(1/2)},d,b >

B_{ij} = ( <a,0,b>,<0,a,d>,<b,d,a> )

det[B_{ij}+(-x)·Id_{33}] = (a+(-x))( (a+(-x))^{2}+(-1)·(b^{2}+d^{2}) ) = 0

( X_{ij} )^{o(-1)} o B_{ij} o X_{ij} = ...

... < a+( b^{2}+d^{2} )^{(1/2)},0,0 >,< 0,a,0 >,< 0,0,a+(-1)·( b^{2}+d^{2} )^{(1/2)} >

C_{ij} = ( <a,d,b>,<d,a,d>,<b,d,a> )

det[C_{ij}+(-x)·Id_{33}] = (a+(-x))( (a+(-x))^{2}+(-1)·b^{2} ) = 0

( X_{ij} )^{o(-1)} o C_{ij} o X_{ij} = ...

... < a+b,0,0 >,< 0,a,0 >,< 0,0,a+(-b) >

D_{ij} = ( <a,0,b>,<0,c,0>,<b,0,a> )

det[D_{ij}+(-x)·Id_{33}] = (c+(-x))( (a+(-x))^{2}+(-1)·b^{2} ) = 0

( X_{ij} )^{o(-1)} o D_{ij} o X_{ij} = ...

... < a+b,0,0 >,< 0,c,0 >,< 0,0,a+(-b) >

A_{ij} = ( <a,d,b>,<d,a,0>,<b,0,a> )

x = a+(-1)·(b+d) & y = a+(-d) & z = a+(-b)

det[A_{ij}+(-1)·<x,y,z>·Id_{33}] = 0

det[A_{ij}+(-1)·<a+(-1)·(b+d),a+(-d),a+(-b)>·Id_{33}] = ...

... (b+d)·db+(-1)·bbd+(-1)·ddb = 0

Y_{ij} = ( <x,(-x),(-x)>,<0,y,0>,<(-x),x,z> )

Z_{ij} = ( <(-z),0,(-x)>,<x,y,x>,<(-x),0,(-x)> )

det[Y_{ij}] = det[Z_{ij}]

A_{ij} o Y_{ij} = ...

... ( <ax+b·(-x),a·(-x)+dy+bx,a·(-x)+bz>,...

... <dx,d·(-x)+ay,d·(-x)>,...

... <bx+a·(-x),b·(-x)+a·x,b·(-x)+az> )

Z_{ij} o A_{ij} o Y_{ij} = ...

... ( <(a+(-b))·(1/y)·det[Y_{ij}],dzy+((-a)+b)·(1/y)·det[Y_{ij}],b(z^{2}+x^{2})>,...

... <dx,ay^{2},d(-x)y+(a+b)·(1/y)·det[Y_{ij}]>,...

... <0,d(-x)y,((-a)+(-b))·(1/y)·det[Y_{ij}]> )

Base de Jordan:

y = 1

z = ( (-1)·x^{2}+(1/b) )^{(1/2)}

( (-1)·x^{2}+(1/b) )^{(1/2)} = x

x != ( 1/(2b) )^{(1/2)} & x != (-1)·( 1/(2b) )^{(1/2)}

Z_{ij} o A_{ij} o Y_{ij} = ...

... ( <a·det[Y_{ij}],dz+(-a)·det[Y_{ij}],0>,...

... <dx,a,d(-x)+a·det[Y_{ij}]>,...

... <0,d(-x),(-a)·det[Y_{ij}]> )+...

... ( <(-b)·det[Y_{ij}],b·det[Y_{ij}],1>,...

... <0,0,b·det[Y_{ij}]>,...

... <0,0,(-b)·det[Y_{ij}]> )

det[Y_{ij}] = y·( xz+(-1)·(-x)(-x) )

C_{ij} = ( <a,d,b>,<d,a,d>,<b,d,a> )

x = a+(-b) & y = a+( d^{2}/b ) & z = a+(-b)

det[C_{ij}+(-1)·<x,y,z>·Id_{33}] = 0

det[C_{ij}+(-1)·<a+(-b),a+( d^{2}/b ),a+(-b)>·Id_{33}] = 0

Y_{ij} = ( <(-d)·x,2bx,(-d)·x> )