- #1
MathematicalPhysicist
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i have this matrix:
and i need to find the matrix jordan basis, and jordan form.
for the jordan bassis i need first to find the eigen value which is zero.
i also found that: Ker(A)={e_1} Ker(A^2)={e_1,e_2} Ker(A^3)=R^3
now Ae1=0, Ae2=e1, Ae3=e1+e2.
now the basis must include e2 and e1, cause we have a transformation from e_2 in Ker(A^2) to e_1 in ker(A), but we don't have a transformation from Ker(A^3) to Ker(A^2), Ae3 should be one of either e2 or e1, can someone help me on this?
thanks in advance.
Code:
011
001
000
for the jordan bassis i need first to find the eigen value which is zero.
i also found that: Ker(A)={e_1} Ker(A^2)={e_1,e_2} Ker(A^3)=R^3
now Ae1=0, Ae2=e1, Ae3=e1+e2.
now the basis must include e2 and e1, cause we have a transformation from e_2 in Ker(A^2) to e_1 in ker(A), but we don't have a transformation from Ker(A^3) to Ker(A^2), Ae3 should be one of either e2 or e1, can someone help me on this?
thanks in advance.