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Topic: matrix analysis: can I say matrix X=Y if I have AXA=AYA?
Replies: 8   Last Post: Mar 12, 2004 9:37 AM

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Francis Harrington

Posts: 65
Registered: 12/6/04
Re: matrix analysis: can I say matrix X=Y if I have AXA=AYA?
Posted: Mar 10, 2004 4:32 PM
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"Alexander Malkis" <alexloeschediesmalk@line.cs.uni-sb.de> wrote in message
news://c2nuc6$18r7$1@hades.rz.uni-saarland.de...
> 1. the dimensions of A,X,Y should be compatible, in this case I think
> they should be all square matrices.
>
> 2. If you require that AXA=AYA for all matrices A, then it would
> certainly hold for A=identity matrix.
>
> 3. If A is some unknown matrix, i.e. then AXA=AYA tells you not much.
> E.g. if A=[0]
>

Hi!

Where has my reasoning gone wrong here? Suppose all matrices are square,
and that AXA = AYA is true. If I pre- and post-multiply both sides by A-inv,
I
get X = Y. Thanks for your advice on this.

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