Re:The Philosophy of Linear Algebra (2021)
by threatofrain on Sunday June 12, 2022 @02:48AM
(#31712156)
> 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.
>Computers certainly helped accelerate the development of linear algebra and vice-versa.
Computers have helped with matrix analysis given floating point constraints inherit to computers. But linear algebra has been in a pretty solid place as theory since Halmos published "Finite Dimensional Vector Spaces" in 1942.