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> 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.




Yeah, 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).




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