3 ms·
A related remark: there is another (rather silly) way to "geometrize linear algebra". It goes something like whenever you see a ring R, think of it as the sheaf
by dbranes 9y ago
A related remark: there is another (rather silly) way to "geometrize linear algebra". It goes something like whenever you see a ring R, think of it as the sheaf of functions (the structure sheaf) on some space. Whenever you see a module over R, think of it as the space of sections in some vector bundle over that space. Then anything you say about modules through this admits a sheaf-theoretic version, which is often easier to picture if you're geometrically inclined.
- joppy 9y agoIn the case where the base ring R is a field (all of typical linear algebra), then the space associated to it is a point. So a vector bundle over this point is just a vector space, so we didn't really gain any extra geometry here - if you want a way of picturing linear algebra geometrically, you still need some other idea.
- dbranes 9y agoGood point!