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Revision as of 01:39, 28 April 2009 editRadjenef (talk | contribs)394 edits f^\dagger← Previous edit Revision as of 07:36, 26 May 2009 edit undo130.54.16.83 (talk)No edit summaryNext edit →
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It may help to make the article more useful if somebody (more proficient at this than I) adds what is f^\dagger in each of the examples. It may help to make the article more useful if somebody (more proficient at this than I) adds what is f^\dagger in each of the examples.
:All the dagger does is reverse the direction of arrows. So, if <math>f : A \longrightarrow B</math>, then <math>f^\dagger : B \longrightarrow A</math>. I will have a look at the examples... --] (]) 01:39, 28 April 2009 (UTC) :All the dagger does is reverse the direction of arrows. So, if <math>f : A \longrightarrow B</math>, then <math>f^\dagger : B \longrightarrow A</math>. I will have a look at the examples... --] (]) 01:39, 28 April 2009 (UTC)

:: In Hilb, f^\dagger is given by the adjoint of f, in Rel it is given by the opposite relation, and in the category of finitely generated projective modules it is... what, the transpose of the matrix representation of a linear map?

Revision as of 07:36, 26 May 2009

It may help to make the article more useful if somebody (more proficient at this than I) adds what is f^\dagger in each of the examples.

All the dagger does is reverse the direction of arrows. So, if f : A ⟶ B {\displaystyle f:A\longrightarrow B} , then f † : B ⟶ A {\displaystyle f^{\dagger }:B\longrightarrow A} . I will have a look at the examples... --Radjenef (talk) 01:39, 28 April 2009 (UTC)
In Hilb, f^\dagger is given by the adjoint of f, in Rel it is given by the opposite relation, and in the category of finitely generated projective modules it is... what, the transpose of the matrix representation of a linear map?