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MathGroup Archive 1995

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Re: Complex Matrices

  • To: mathgroup at smc.vnet.net
  • 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 ralph.vnet.net>, David A Boyd
<dab8g at kelvin.seas.virginia.edu> 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
real.


In[1]:=
    m = {{a + I b, c + I d},{e + I f, g + I h}}
Out[1]=
    {{a + I b, c + I d}, {e + I f, g + I h}}
In[2]:=
    Conjugate[ m ]
Out[2]=
    {{Conjugate[a + I b], Conjugate[c + I d]}, 
 
      {Conjugate[e + I f], Conjugate[g + I h]}}
In[3]:=
    ComplexExpand[ %]
Out[3]=
    {{a - I b, c - I d}, {e - I f, g - I h}}

In[4]:=
    ?ComplexExpand

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
   complex.

I hope this helps.

--Ian


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