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Halmos are always good books. I didn't know he had this viewpoint on determinants though. What I meant is that on a pure mathematical point of view they are se
by somethingsome 6y ago
Halmos are always good books. I didn't know he had this viewpoint on determinants though.
What I meant is that on a pure mathematical point of view they are seen as inelegant as they require a basis to be defined. I don't have a problem with that when you are doing maths on manifolds etc..
From a practical perspective, a lot of engineering problems go from 1 to 4 dimensions and are basis dependents. And the determinant becomes a useful tool.
- llamaz 6y agoHe doesn't have a particular view on determinants, I got my views on determinants more from Axler than from Halmos. But Halmos' book is linear algebra as preparation for functional analysis, so he tends not to choose a basis for proofs. I agree with you, that in practical paper computations (e.g. on exams) that determinants are an indespensible practical tool.