5 ms·
> I now feel not only that I don’t like determinants but that I’m allergic even to matrices Determinants are totally basis-invariant, however, similar matrices
by Tainnor 2y ago
> I now feel not only that I don’t like determinants but that I’m allergic even to matrices
Determinants are totally basis-invariant, however, similar matrices have the same determinant.
- xanderlewis 2y agoYeah, and I think that’s enough motivation for determinants being important beyond as a computational trick. I was being somewhat hyperbolic. Seeing the determinant as the unique solution to the problem of assigning a scalar to each linear map/matrix in such a way that several natural axioms are satisfied is a very nice way to motivate it. Along with the fact that it, along with the trace, can be calculated from the eigenvectors (from which the basis-invariance is clear).