You would like to find all such that
or equivalently
.
Now you should see that you need to find
and this is your eigenspace
I needed to find the eigenvalues for the matrix
5 0 1
1 1 0
-7 1 0
Which I found to be 2 with multiplicity 3.
Now I am required to find the eigenspace, and therein describe it geometrically.
I believe that I am supposed to use this:
det(2I-A)=0
and then subsequently row reduce the augmented matrix to find the solution.
I end up with an identity matrix with a column of zeroes, which would then mean that the matrix has only the trivial solution. Have I done this incorrectly? And if not, how do I describe this geometrically?
Have a peruse of this.
http://en.wikipedia.org/wiki/Kernel_(matrix)