Eigenvectors

OldManJenkin

I've tried to calculate the eigenvectors of the matrix
[LATEX]
A=
\bordermatrix{&&&\cr
&1&0&0\cr
&0&0&0\cr
&0&0&-1\cr}


[/LATEX]
and I've found the eigenvalues to be 0, 1 and -1 (Wolfram Alpha agrees.)

For the eigenvector with eigenvalue zero, you get

[LATEX]
A=
\bordermatrix{&&&\cr
&1&0&0\cr
&0&0&0\cr
&0&0&-1\cr}
\bordermatrix{&\cr
&x\cr
&y\cr
&z\cr}=0
[/LATEX]

How do you find out what y is; do you just assume that it can be any number?

Thanks

TheBody

You are just solving a system of equations to find the eigenvector. As there is no leading 1 in the y column, that tells you that y will be a free variable. So you are right, you can say something like let [latex]y=t[/latex] where [latex]t \in \mathbb{R}[/latex].

OldManJenkin

Thanks!

TheBody

Glad I could help!!