If you plan to do calculations using vectors, you should consider using some CPAN module as Math::Vector::Real. For instance:

use Math::Vector::Real;

my @data = map V(split), grep /\S/, <IN>;

for my $i (0 .. $#data) {
  my $u = $data[$i]
  for my $j (0 .. $#data) {
    next if $i == $j;
    my $v = $data[$j];
    my $dist = $u->dist($v);
    print OUT "%s to %s Distance-%.5f\n", $u, $v, $dist;
  }
}
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PDL is another interesting tool for numeric intensive computations. It has a somewhat steep learning curve, but in the end it is quite productive.