Manually multiplying
(1+i)(3+i) + (2+i)(2+i) = 5+8i
(1-2i)(3+i) +(2-i)(2+i) = 10-5i

These two equations can be expressed in terms of the matrix equation MX = B, where

       / 1+i    2+i \         / 3+i \                /  5+8i \
M = |                |   X = |       |   and B = |           |
       \1-2i    2-i  /         \ 2+i /                \ 10-5i  /
[download]

One should therefore be able to use complex piddles to obtain B by multiplying M times X, or alternatively obtain X by multiplying the inverse of M times B using the following code:

#! /usr/bin/perl -w
use warnings;
use strict;    
use PDL;
use PDL::Complex;

my $matrixM = pdl [ [ 1+1*i, 2+1*i],
                               [ 1-2*i, 2-1*i] ];
my $matrixB_assigned_value = pdl [ 5+8*i,
                                                     10-5*i ];
my $matrixX_assigned_value = pdl [ 3+1*i,
                                                      2+1*i ];
my ($matrixB_computed_value, $matrixX_computed_value);

print "Via Perl Data Language\n";
print "List assigned_values of matrices:\n";
print "\$matrixM = ", $matrixM,"\n";
print "\$matrixX_assigned_value = ", $matrixX_assigned_value,"\n";
print "\$matrixB_assigned_value = ", $matrixB_assigned_value,"<br>\n";
print "List computed values of matrices:\n";
print "\$matrixB_computed_value = ", 
                          $matrixM x $matrixX_assigned_value,"\n";
print "\$matrixX_computed_value = ", 
                         $matrixM->inv x $matrixB_assigned_value,"\n";
exit(0);
[download]

When the above code is executed, the following output is created:

Via Perl Data Language
List assigned_values of matrices:
$matrixM =
[
 [
  [1 1]
  [2 1]
 ]
 [
  [ 1 -2]
  [ 2 -1]
 ]
]

$matrixX_assigned_value =
[
 [3 1]
 [2 1]
]

$matrixB_assigned_value =
[
 [ 5  8]
 [10 -5]
]
<br>
List computed values of matrices:
$matrixB_computed_value =
[
 [
  [5 2]
  [8 3]
 ]
 [
  [-1 -1]
  [ 4  1]
 ]
]

$matrixX_computed_value =
[
 [
  [  5 -13]
  [  0  21]
 ]
 [
  [ 5 -6]
  [ 0 -7]
 ]
]
[download]

Notice how the assigned values for M, X, and B dutifully print as expected. However the computed values for X and B are strange. Please can you explain what I need to change to correctly compute the values of X and B in my little example.

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