[notthingnill]

Apart from Gauss elimination, I think eigenvalues, eigenvectors, scalar product, orthogonal subspaces, and the relation to statistics are important. Statistics associated with SVD, principal components and other topics are a main source of insights. Also Fourier basis is an important concept far beyond Gauss elimination.

[throwawaymath]

Of course, I'd agree. But my comment is pretty long as it is, and is more concerned with the arrangement of material than how many extended topics you cover. I'm treating perfection as nothing left to remove, not nothing left to add :)