       Re: Incomplete simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg49287] Re: [mg49285] Incomplete simplification
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 12 Jul 2004 02:11:28 -0400 (EDT)
• References: <200407110616.CAA16721@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 11 Jul 2004, at 15:16, Carlos Felippa wrote:

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> Using Mathematica 4.2 on a mac I defined a 6 x 3 symbolic
> matrix and take its Moore-Penrose inverse:
>
> S={{0,-x31,x21},{x31,0,-x11},{-x21,x11,0},{0,-x32,x22},
>       {x32,0,-x12},{-x22,x12,0}};
> G=PseudoInverse[S];
>
> Mathematica thinks the entries are complex, so it returns a
> result with Conjugate[x11], etc.  To get rid of them I tried
>
> G=Simplify[G,x11\[Element]Reals&&x21\[Element]Reals   <...> ];
>
> But the Conjugate[...] are still there. Fortunately G=ComplexExpand[G]
> works. But why is Simplify unable to use the reality assumptions?

In my case (both in Mathematica 5.0 and 4.2)

S = {{0, -x31, x21}, {x31, 0, -x11}, {-x21, x11, 0}, {0, -x32, x22},
{x32, 0, -x12}, {-x22, x12, 0}};

G = PseudoInverse[S];

Simplify[G, Element[_, Reals]]

produces an answer without any Conjugates. Sounds like there was