> We share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.
It's long joked that much pure math research is resolving really hard problems down to a calculus or linear algebra computation.
When I first learned differential geometry, I was enamored with all the stuff we could do without coordinates. Then I learned Riemannian geometry and felt like I had been duped.
~ Irving Kaplansky