Timeline for Inverse of a matrix over a non-commutative ring
Current License: CC BY-SA 3.0
7 events
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| Nov 27, 2011 at 8:25 | comment | added | Alan Swindells | One other point: most matrix inversion algorithms, eg LUD use the concept of relative magnitude to find the largest pivot. Is the det of the individual elements a valid proxy for this? What about if the elements are say polynomials where there is no such concept? | |
| Nov 27, 2011 at 8:19 | comment | added | Alan Swindells | Thanks. It's a bit too advanced for me but I'll have some fun trying to figure it out! | |
| Nov 26, 2011 at 18:28 | comment | added | Alexander Chervov | The example is LU decomposition - you express the elements of L and U in terms of the elements of inverse matrix (i.e. quasi-dets). | |
| Nov 26, 2011 at 18:27 | comment | added | Alexander Chervov | The survey on quasi-dets: arxiv.org/abs/math/0208146 See also arxiv.org/abs/q-alg/9705026. | |
| Nov 26, 2011 at 18:27 | comment | added | Alexander Chervov | Quasi-det is NOT direct analogue of the determinant in the commutative case. It is very simple thing. There are by definition not one, but n^2 quasi-determinants. Quasi-determinant with index (i,j) is by definition the (i,j) element of the inverse matrix. More precisely you should invert this element. So you may ask why such a simple thing should be called by loud name "quasi-determinant". The logic of authors (imho) - that for many matrix theorems you do not need determinant, but key thing is inverse matrix and you can reformulate in terms of its elements (i.e. quasi-dets) some theorems | |
| Nov 26, 2011 at 16:12 | comment | added | Alan Swindells | Great, that sounds like what I am looking for. I'll try and find the papers that cover it. Thanks | |
| Nov 26, 2011 at 14:46 | history | answered | user6976 | CC BY-SA 3.0 |