I'm asked to find a basis for $W$, which is a subspace of $M_n(F)$.
$W$ is the subspace containing all upper triangular $n \times n$ matrices.
How do you find this basis?
My guess is that it's simply a collection of $[n(n+1)]/2$ matrices $E^{ij}$ in which $ij = 0: i>j$.
Would that be correct, and if so, is there a better way to express it? How do I show that it spans?