Timeline for A textbook on linear algebra where involutions on linear spaces are considered
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 7, 2013 at 14:39 | comment | added | Sergei Akbarov | This will be my handbook. Like Bible. :) | |
| Jul 7, 2013 at 14:07 | comment | added | Sergei Akbarov | It is easy to prove of course, but it is not good to write this proof in a paper, or to use this result without reference. Ben, I don't like the formulation of this fact that Fulton and Harris give at p.444. This is not for normal mathematician, you must have some background in representation theory to recognize what I need in what they say. I believe there are texts with simpler formulations. And, by the way, I need also the constructions of real and imaginary parts, and their properties. Of course this is trivial, but I'd like to have a book on my table. | |
| Jul 7, 2013 at 13:54 | comment | added | Ben McKay | This equivalence is stated in Fulton and Harris, p. 444. But it is easy to prove anyway. | |
| Jul 7, 2013 at 13:51 | comment | added | Sergei Akbarov | "a complex vector space is the complexification of a real vector space just when it bears a conjugate linear involution operator" -- I need this and the construction of involution on the dual space. But I think it's not nice to write this without reference. Or you mean that this is stated in the Fulton-Harris book? | |
| Jul 7, 2013 at 13:39 | comment | added | Ben McKay | Which properties do you need? As a I wrote above, a complex vector space is the complexification of a real vector space just when it bears a conjugate linear involution operator; the real vector space is the set of fixed points of the involution. So the category of conjugate linear involutions is isomorphic to the category of real vector spaces, and the properties are just those of real vector spaces. There can't be any more or fewer properties. | |
| Jul 7, 2013 at 11:05 | comment | added | Sergei Akbarov | I do not understand. I need a source for reference, the book must contain a list of properties of this notion. | |
| Jul 7, 2013 at 10:02 | history | answered | Ben McKay | CC BY-SA 3.0 |