- #1
jejaques
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Hello! I'm trying to do some linear algebra. I have an insane Russian teach whose English is, uh, lacking.. so I'd appreciate any help with these I can get here!
Find the canonical forms for the following linear operators and the matrices for the corresponsing change of coordinates.
Here is the 6x6 matrix:
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
-1 0 0 -2 0 0
I know I have to do subtract [tex]\lambda[/tex] on the diagonal, take the determinant, find the roots by solving for the [tex]\lambda[/tex] values, and then plug them in one at a time to find the different [tex]\zeta[/tex], turn that into a change of coordinates, and then depending on case, put it into canonical form...
Unfortunately, my professor has only shown us the various [tex]\lambda[/tex] cases for 2 x 2 matrices and because we can "look everything up on google," we have no book!
A couple questions: Can I simplify this or maybe turn it into the Jordan block? Can anyone point me to a similar problem, even? I've been searching for two hours, have searched through three free linear algebra e-books and am still lost =(
Thanks so much!
Homework Statement
Find the canonical forms for the following linear operators and the matrices for the corresponsing change of coordinates.
Here is the 6x6 matrix:
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
-1 0 0 -2 0 0
Homework Equations
The Attempt at a Solution
I know I have to do subtract [tex]\lambda[/tex] on the diagonal, take the determinant, find the roots by solving for the [tex]\lambda[/tex] values, and then plug them in one at a time to find the different [tex]\zeta[/tex], turn that into a change of coordinates, and then depending on case, put it into canonical form...
Unfortunately, my professor has only shown us the various [tex]\lambda[/tex] cases for 2 x 2 matrices and because we can "look everything up on google," we have no book!
A couple questions: Can I simplify this or maybe turn it into the Jordan block? Can anyone point me to a similar problem, even? I've been searching for two hours, have searched through three free linear algebra e-books and am still lost =(
Thanks so much!