Timeline for Representing quaternions as matrices
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2013 at 6:28 | comment | added | Andrew | yep, It's my condition. So that isomorphism is as I told above? | |
| Jun 1, 2013 at 14:00 | comment | added | Name | An isomorphism between the generalized quaternion algebra $(a,b)_F$ and $M_2(F)$ only exists if the the form $x^2-ay^2-bz^2+abt^2$ has a nontrivial zero. | |
| Jun 1, 2013 at 13:12 | comment | added | Andrew | can we choose subfield closed so q^2=-a and p^2=-b hence we have representation i=((q,0),(0,-q)) and j=((0,p),(-p,0))? | |
| Jun 1, 2013 at 13:04 | comment | added | Andrew | ok, how to represent generalised quaternions A(a,b) using 2*2 matrices? I need this, cuz I want to prove isomorphism between generalised quaternions over F and matrix 2*2 over F. Thanks! | |
| Jun 1, 2013 at 12:57 | comment | added | KConrad | The Artin-Wedderburn theorem doesn't claim there is a representation as 2 x 2 matrices. Take Hamilton's quaternions $A(-1,-1)$ with $F = {\mathbf R}$. The usual representation with matrices uses 4 x 4 real matrices or 2 x 2 complex matrices. | |
| Jun 1, 2013 at 12:52 | comment | added | Andrew | But Artin–Wedderburn theorem claim that there is 2*2 matrix over F exists. | |
| Jun 1, 2013 at 12:45 | history | answered | Abhinav Kumar | CC BY-SA 3.0 |