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> 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.

~ Irving Kaplansky




Ha! True enough.

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.




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