Timeline for Iwasawa Decomposition for Matrices [closed]
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 16, 2013 at 10:27 | history | closed |
R W John Pardon David White Andrey Rekalo Chris Godsil |
Not suitable for this site | |
| Aug 16, 2013 at 3:04 | review | Close votes | |||
| Aug 16, 2013 at 10:27 | |||||
| Aug 12, 2013 at 14:07 | comment | added | Emerton | Dear Vishal, This is the Gram--Schmidt process for turning a basis of $\mathbb R^n$ into an orthonormal basis: think of the columns of a matrix in $GL_n(\mathbb R)$ as a basis of $\mathbb R^n$, apply Gram--Schmidt, and then reinterpret it in terms of matrix multiplications. (This is basically what Paul Garrett's answer does.) Regards, | |
| Aug 11, 2013 at 18:32 | vote | accept | Vishal Gupta | ||
| Aug 11, 2013 at 18:23 | vote | accept | Vishal Gupta | ||
| Aug 11, 2013 at 18:23 | |||||
| Aug 11, 2013 at 17:52 | answer | added | paul garrett | timeline score: 6 | |
| Aug 11, 2013 at 17:43 | comment | added | Vishal Gupta | Could you please give a more elementary argument using only matrices? | |
| Aug 11, 2013 at 17:10 | comment | added | JGordon | Sorry about my previous (now deleted) comment, where I completely misread the question. It is, indeed, the special case of the Iwasawa decomposition; the general proof is Proposition 7.31 in Knapp's "Lie groups beyond an introduction", for example. First, we can reduce it to $SL_n$ and $S0_n$, respectively. Now, the idea is to first see the decomposition on the Lie algebra level, and then show that the image of $T\times SO$ has to be open (this uses the Lie algebra decomposition) and closed (this is easy to see since $SO$ is compact) in $SL_n$. This might be an overkill though. | |
| Aug 11, 2013 at 16:52 | review | Close votes | |||
| Aug 11, 2013 at 17:24 | |||||
| Aug 11, 2013 at 16:35 | history | edited | BS. |
removed tag functional-analysis
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| Aug 11, 2013 at 16:06 | history | asked | Vishal Gupta | CC BY-SA 3.0 |