Timeline for Moore-Penrose Inverse as an adjoint
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2012 at 17:26 | comment | added | Nicolas Schmidt | Oops ..., I didn't realize Moore-Penrose inverses don't compose! | |
| Jun 12, 2012 at 17:25 | vote | accept | Nicolas Schmidt | ||
| Jun 9, 2012 at 19:47 | history | edited | Michal R. Przybylek | CC BY-SA 3.0 |
typos
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| Jun 9, 2012 at 19:46 | comment | added | Michal R. Przybylek | Qiaochu, I meant that if you defined a pseudoinverse as an adjunction (plus some additional conditions), then it would not be a categorical concept. This is because (gf)^+ have to be isomorphic (that is 2-isomorphic, for any chooice of 2-isomorphisms) to f^+g^+, yet at the same time it may not be a pseudoinverse. | |
| Jun 9, 2012 at 18:51 | comment | added | Qiaochu Yuan | I'm not sure what you mean when you say that pseudoinverses aren't categorical. The definition can be phrased in a purely categorical manner in any dagger category so ought to be invariant under unitary isomorphisms (isomorphisms $\phi$ such that $\phi^{\dagger} = \phi^{-1}$). | |
| Jun 9, 2012 at 14:17 | history | answered | Michal R. Przybylek | CC BY-SA 3.0 |