Halmos are always good books. I didn't know he had this viewpoint on determinants though.

What I meant is that on a pure mathematical point of view they are seen as inelegant as they require a basis to be defined. I don't have a problem with that when you are doing maths on manifolds etc..

From a practical perspective, a lot of engineering problems go from 1 to 4 dimensions and are basis dependents. And the determinant becomes a useful tool.