
Re: matrix analysis: can I say matrix X=Y if I have AXA=AYA?
Posted:
Mar 10, 2004 4:04 PM


In article <c2nuc6$18r7$1@hades.rz.unisaarland.de>, Alexander Malkis <alexloeschediesmalk@line.cs.unisb.de> wrote: >1. the dimensions of A,X,Y should be compatible, in this case I think >they should be all square matrices.
Not at all.
For AXA to make sense, where X is n x m, we need A to be ? x n (so we can multiply A by X), but it must also be m x ? (so we can multiply X by A). Set A to be m x n, and everything works out. Clearly, then Y should by n x m, same size as X. So X and Y should be the same size, but if X and Y are, say, 2 x 3 matrices, then you can let A be a 3 x 2 matrix and all the operations are compatible.
The result on both sides will be an m x n matrix.
 ====================================================================== "It's not denial. I'm just very selective about what I accept as reality."  Calvin ("Calvin and Hobbes") ======================================================================
Arturo Magidin magidin@math.berkeley.edu

