Thread: Subspaces

If I can describe the subspaces of R^3 as being lines, planes, all of R^3, and the zero vector then how can I describe D the space of all 2x2 diagonal matrices?

Would it be correct to say: a "line" of 2x2 diagonal matrices, a "plane" of 2x2 diagonal matrices, all of D, and the zero matrix?

Is there a term for a "line"/"plane" of matrices?
Is there a term for a "line"/"plane" of functions?

Not really. We'll just say "a two-dimensional subspace" instead of a "plane".