Umm, sure. That is a matrix, but I don't see it being much more useful than the four vectors it is made up of. You can put anything (usually numbers, though) in those places and you'll still have a 4x4 matrix.

Understand that a matrix is an abstract concept and has hundreds of common uses, all over science. One could spend lifetimes learning about matrices, in general, and not scratch the surface. In the context of games programming, we generally consider matrices to represent transformations from one vector-space to another.

I strongly suggest you take a look at the vector mathematics primers in the FAQ, as Googling for 'Matrix' could end you up in a bad, bad place.

Regards
Admiral