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Re: Complex Matrices

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  • Subject: [mg2436] Re: Complex Matrices
  • From: ianc (Ian Collier)
  • Date: Wed, 8 Nov 1995 23:42:56 -0500
  • Organization: Wolfram Research, Inc.

In article <47hh8n$dcl at>, David A Boyd
<dab8g at> wrote:

> Here is my problem: I have a matrix, M , with complex elements, and I want
> to find M*.M. If I try Conjugate[ M ].M. or Conjugate[ M[[1,1]] ] M[[1,1]],
> Mathematica will not expand the answer.That is to say instead of having
> all of the I's replaced with -I's, I just get back Conjugate[ M ].M. even
> if I try Expand[].  Which is not a lot of help.
> david

The problem is, probably, that Mathematica does not know if
teh other symbols in your matrix are real or complex.

ComplexExpand forces Mathematica to treat all variables as

    m = {{a + I b, c + I d},{e + I f, g + I h}}
    {{a + I b, c + I d}, {e + I f, g + I h}}
    Conjugate[ m ]
    {{Conjugate[a + I b], Conjugate[c + I d]}, 
      {Conjugate[e + I f], Conjugate[g + I h]}}
    ComplexExpand[ %]
    {{a - I b, c - I d}, {e - I f, g - I h}}


ComplexExpand[expr] expands expr assuming that all variables
   are real. ComplexExpand[expr, {x1, x2, ...}] expands expr
   assuming that variables matching any of the xi are

I hope this helps.


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