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Axlers book is lovely, but my (amateur) opinion is that determinants are pretty damn intuitive and useful in the applied world. They appear quite naturally in t
by forkandwait 9y ago
Axlers book is lovely, but my (amateur) opinion is that determinants are pretty damn intuitive and useful in the applied world. They appear quite naturally in the systems of equations I have worked with.
Furthermore, some would argue that mathematics has lost its way as it becomes dedicated to abstraction alone.
- hidenotslide 9y agoI don't understand, can you give an example? For most of the classical applications determinants are computationally terrible compared to factorization methods, e.g. for matrix inverse elimination is O(n^3) and Cramer's rule is something like O(n!).
- tgb 9y agoI think it's false to equate determinants with "determinants computed by cofactor expansion". One can compute determinants efficiently through Gauss elimination, too.
- hidenotslide 9y agoFair, but I'm still not aware of any practical applications for "systems of equations" like the person I responded to mentioned. If you know any please share. The determinant intuition for me is the signed volume factor for a change of basis. I've seen the combinatorial lattice path application and I'm sure there are more in other fields. But not much reason I can see to have them feature so prominently in an intro linear algebra class. Better to spend more time with SVD for instance, which wasn't even covered in the first linear algebra class I took.