Hey, I was wondering if someone could help me find a basis for the space of all nxn matricies, over R, with trace 0.
It's been a long while, but maybe I can give a small push. Take this with a grain of salt
We know that
If then all .
A basis for the space of all nxn matricies, then, is the set of all matricies with 1 as an ij-th entry **, and all the rest being 0. go through all the possibilities.
ex. for a 2x2 matrix, the basis would be
and
EDIT:// ** with