The matrix is represented as an array of arrays.
Add a use Data::Dumper; statement, then various print Dumper \@square_matrix; statements to see how the data is being represented. 
example of a 3x3:
my @m = ([0,0,0],
         [0,0,0],
         [0,0,0]);

[download]
Each "row" is what the [@x] represents and is the return value of the map. Another set of code in this thread uses a hash table to represent the data.

The main idea is to make a square matrix and then each set of letters results in two entries into that matrix. Many implementations of that idea are possible, some much shorter than what I did in this case.

Update:

This might help you to understand what is going on without a map...a map is kind of like a "tricky" foreach() loop. 

#!/usr/bin/perl -w
use strict;
use Data::Dumper;

my @sq_matrix_3x3;

my @list = (1,2,3);
foreach (@list)        
{
    push (@sq_matrix_3x3, [0,0,0]); #creates a row with 3 elements
}
print "3x3 Matrix: ";
print Dumper \@sq_matrix_3x3;

[download]
This is the same thing and perhaps a more familiar form of [x][y] coordinates 
my @another_2D;
for (my $x=0; $x<3; $x++)
{
  for (my $y=0; $y<3; $y++)
  {
     $another_2D[$x][$y]=0;
  }
}
print Dumper \@another_2D;
__END__
prints:
3x3: $VAR1 = [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ];
# print Dumper \@sq_matrix_3x3; #these both produce the same output
# print Dumper \@another_2D;

[download]

In reply to Re^3: creating adjacency matrix by Marshall
in thread creating adjacency matrix by ramdat

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