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📁 [[ Complex Matrices : Language c]]
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<TITLE> Mathematic : Complex Matrix : Language C. </TITLE>
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<A HREF="http://groups.yahoo.com/group/mathc/">Mathc</A> : This group work on numerical computation. You can find free source code to download.

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<A HREF="http://www.geocities.com/xhungab/tutorial.html">Tutorial</A>,
<A HREF="http://www.geocities.com/xhungab/calculus.html">Calculus</A>,
<A HREF="http://www.geocities.com/xhungab/package.html">Linear Algebra</A>,
<A HREF="http://www.geocities.com/xhungab/gnuplot.html">Gnuplot</A>. The other packages, 

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<H4><U>Complex</U> :  Language C (version  2003/10/09).</H4>
 * You need a C compiler to compile the code (source).</br> 
 * For this work, I use  
   <A HREF="http://www.simtel.net/pub/pd/17456.html">Dev-C++ 4</A>, 
   and 
   <A HREF="http://www.delorie.com/djgpp/zip-picker.html">DJGPP</A> two freewares. </br> 
 * You can also use 
   <A HREF="http://www.softintegration.com">Ch 4.0 released</A> (C99). 
   The Standard Edition is free in all platforms. </br> 
 * The graphic interface is gnuplot.</br>
 * You can download this freeware here : <A HREF="http://www.gnuplot.info/">Gnuplot Central</A>. </br>
 * My work is also a Freeware.</br> 
 * Windows, Linux.</br>

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<H4><U>Complex Numbers</U>.</H4></P> 
<A HREF="http://www.geocities.com/xhungab/complex/cz01a.zip">cz01a.zip</A> :         
 add, sub, multiply, divide, inverse, conjugate, symetric, abs.</br>

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<H4><U>Complex Matrices</U>.</H4></P> 
<A HREF="http://www.geocities.com/xhungab/complex/cm01a.zip">cm01a.zip</A> :</P>         
       add, subtract, multiply, conjugate, conjugate transpose, trace,</br>
       determinant, cofactor, matrix of cofactor, adjoint, inverse,</br> 
       gauss, gaussjordan, LU decomposition, with complex values,</br>
       Euclidian inner product, norm, distance  in C**n, in Mnm, </br>
</br>

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<H4><U>Verify with numeric applications</U>:</H4>

<A HREF="http://www.geocities.com/xhungab/complex/cm03a.zip">cm03a.zip</A> :
Vector space axioms on  (rows, columns) vectors with complex coeffients.</P> 

<A HREF="http://www.geocities.com/xhungab/complex/cm03d.zip">cm03d.zip</A> :</P>
      * The properties of the conjugate transpose.</br>
      * The theorem of the conjugate transpose.</br>
      * The theorem of inverse matrices.</br>
      * (A+B)**2, (A-B)**2, (A-B) (A+B).</P>


<A HREF="http://www.geocities.com/xhungab/complex/cm03b.zip">cm03b.zip</A> :</P>
                   * Properties of Euclidian inner product in C**n.</br>
                   * Properties of distance in C**n.</br>
                   * u.v = 1/4 ||u+v||**2  -  1/4 ||u-v||**2 + i/4 ||u+iv||**2  - i/4 ||u-iv||**2. </br>
                   * If u.v =0 :  ||u+v||**2 = ||u||**2 + ||v||**2.</P>

<A HREF="http://www.geocities.com/xhungab/complex/cm03c.zip">cm03c.zip</A> :</P>
                   * Properties of inner product in Mmn with complex coefficients.</br>
                   * Properties of distance in Mmn with complex coefficients.</br>
                   * u.v = 1/4 ||u+v||**2  -  1/4 ||u-v||**2 + i/4 ||u+iv||**2  - i/4 ||u-iv||**2. </br>



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<HR><H4><U>Application</U>:</H4>               
<A HREF="http://www.geocities.com/xhungab/complex/cm04a.zip">cm04a.zip</A> :
 Verify with numeric applications, some properties of the Dirac matrices..</br>


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