As a mental exercise, I wanted to see if I could use PDL's matrix functions to do this. My idea was to transpose the matrix, add it to itself, then subtract the original diagonal. This would extend it's usefullness to huge arrays. I got as far as adding the transpose to itself, and getting the original diagonal, which would be then be zero padded, and subtracted from the result of the matrix addition.

This might be a way to go, if you want to use a module.

#!/usr/bin/perl
use warnings;
use strict;
use PDL::LiteF;

my $a = pdl([ 
          [1,   ,     ,     ],
          [4,  -5,    ,     ],
      [7,  -8,   -9,    ],
      [17, -18, -90,  114],
      ]);

print $a,"\n";

my $b = transpose($a);
print "$b\n";

my $c = $a+ $b;
print "$c\n";

my $d = $a->diagonal(0,1);
print "$d\nNeeds to be padded with zeros and subtracted from  \$c\n";

print "I'll leave that to you. :-)\n";
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