       Re: Solving a symbolic complex linear system of equation.

• To: mathgroup at smc.vnet.net
• Subject: [mg77944] Re: Solving a symbolic complex linear system of equation.
• From: Szabolcs <szhorvat at gmail.com>
• Date: Wed, 20 Jun 2007 05:33:23 -0400 (EDT)
• Organization: University of Bergen
• References: <f58dlb\$8lc\$1@smc.vnet.net>

```
Please state the question precisely.

Fo wrote:
> Suppose that I want to solve symbolically a system of lienar equations
> defines as:
> \$Ax=B\$ , where A is a complex matrix, B is a complex vector and x is
> the vector of the unkown.

You say you want to solve A x = B.  If A is invertible, the solution is
x = A^-1 B.  Inverse[] can be used to compute A^-1.

> The elements of the A matrix (that is simmetric) are in the form
> \$A_{ij}e^{i phi_{ij}}\$.
> I tried in several ways but I couldn't define the variables \$A_{ij}\$
> and \$ phi_{ij}\$ as real.

Any complex number can be written in the form A Exp[I*phi] (where A and
phi are real), so I do not see the point here.

Or is a '=' sign missing and you mean that all the elements are complex
numbers of magnitude 1?  Even if they are, the solution is still A^-1 B.

Do you mean that you would like to specify that some of the variables
are real when simplifying the end result? For this, look up the syntax
for Simplify[], and use something similar to Simplify[Sqrt[a^2], a
\[Element] Reals] to specify that a variable 'a' is real.

> I tried using the package Algebra`ReIm` and to define each variable as
> z/:Im[z]=0.
> But it does not the wanted result and also I've already read the help
> page for ComplexExpand[].

What kind of result do you expect?  It would be helpful if you posted
the complete problem, with some more detailed explanation.

> Thank you, every suggestion will be helpful.
> Fortu
>
>

```

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