when you compute eigenvalues, the part that you need to form a base . Does the order matter? because i mostly get contradictionary results like
a(1,0,-1) while in the textbook it says a(-1,01) because i extracted an other variable. Does this make a difference? because the next step is combining those bases to do a diagonalization

Question

when you compute eigenvalues, the part that you need to form a base . Does the order matter? because i mostly get contradictionary results like
a(1,0,-1) while in the textbook it says a(-1,01) because i extracted an other variable. Does this make a difference?  because the next step is combining those bases to do a diagonalization

loser66 · Answer

The order of eigenvalues doesn't matter!! but the order of theirs eigenvectors is important!!

ganeshie8 · Answer

If $\large \mathrm{e}$ is an eigenvector for eigenvalue $\lambda$, then any scalar multiple of it, $\large  a \mathrm{e}$ is also an eigenvector of the same eigenvalue $\lambda$

ganeshie8 · Answer

It helps to keep in mind that there is no "the basis" for a vector space
any linearly independent vectors are fine for "a basis"

loser66 · Answer

|dw:1437765054056:dw|

loser66 · Answer

|dw:1437765276787:dw|

loser66 · Answer

got what I mean?

anonymous · Answer

so this is the same base?

ganeshie8 · Answer

what is your actual matrix that you're trying to diagonalize ?

anonymous · Answer

1    3   3 
-3  -5 -3
-3   3    1

anonymous · Answer

everything goes perfect until i need to make bases for my found eigenvalues

loser66 · Answer

Post the original problem, please, by snapshot or scanning!!

anonymous · Answer

attachment

ganeshie8 · Answer

1, -2, -2 are your eigenvalues ?

anonymous · Answer

and this is the  characteristic equation : |dw:1437765738465:dw|