Timeline for Rotation matrices and prior invariance for arbitrary dimensions
Current License: CC BY-SA 2.5
9 events
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| Feb 17, 2011 at 19:44 | history | edited | onestop | CC BY-SA 2.5 |
The diagonal matrix must orthogonal, but every sentence must a verb
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| Feb 17, 2011 at 19:11 | comment | added | cardinal | @whuber, Good catch! Thank you, and I've updated it accordingly. | |
| Feb 17, 2011 at 19:10 | history | edited | cardinal | CC BY-SA 2.5 |
added 91 characters in body; added 9 characters in body
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| Feb 17, 2011 at 18:27 | comment | added | whuber♦ | (+1) @Cardinal One small thing: the resulting diagonal matrix does not need to be the identity. It can have an even number of -1's. But those can be converted to +1's by means of suitable rotations (of 180 degrees). It's also worth nothing the implicit assumption that the only rotations one can use are with respect to a fixed basis. If not, then any rotation can always be written in the form $R_n(\theta)$ (that is, as a single such matrix) by choosing an appropriate basis adapted to that rotation. | |
| Feb 17, 2011 at 15:21 | comment | added | cardinal | @probabilityislogic, Givens rotations are very popular in numerical linear algebra due to their simplicity and good numerical-stability characteristics. Some QR decomposition methods use them and I think any good SVD implementation will use them as well. | |
| Feb 17, 2011 at 15:13 | comment | added | probabilityislogic | Thanks for this, you have saved me a lot of useless algebra! Because I can go "rotation 2-D" new prior invariant... "rotate 2-D" new new prior invariant ..... etc. | |
| Feb 17, 2011 at 15:11 | vote | accept | probabilityislogic | ||
| Feb 17, 2011 at 14:57 | comment | added | probabilityislogic | thanks for your answer, especially the terminology - I've never heard of "givens" rotation before. | |
| Feb 17, 2011 at 14:41 | history | answered | cardinal | CC BY-SA 2.5 |