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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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 magidin@math.berkeley.edu Posts: 11,749 Registered: 12/4/04
Re: matrix analysis: can I say matrix X=Y if I have AXA=AYA?
Posted: Mar 10, 2004 4:04 PM
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In article <c2nuc6\$18r7\$1@hades.rz.uni-saarland.de>,
Alexander Malkis <alexloeschediesmalk@line.cs.uni-sb.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

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