You cannot call a method on an object which does not support that method. Your $H is not a Math::MatrixReal object so it does not support the sym_diagonalize method. Here's a trivial illustration:

#!/usr/bin/env perl 
use strict;
use warnings;
use Math::MatrixReal;
use CGI; # For example

my $cgi = CGI->new;

my $whassat = 'CGI';
print "\$cgi is an object of class $whassat\n" if $cgi->isa ($whassat)
+;

eval { my @res = $cgi->sym_diagonalize; }; # This will fail
print $@ if $@;

my $mmr = Math::MatrixReal->new_from_rows ( [[ 1 .. 3 ], [ 2, -99, 2 ]
+, [ 3, 2, -7]] );
$whassat = 'Math::MatrixReal';
print "\$mmr is an object of class $whassat\n" if $mmr->isa ($whassat)
+;

my @res = $mmr->sym_diagonalize; # This will succeed

print "First Eigenvalue: @{$res[0]->[0][0]}\n";
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If you copy-convert your $H into a Math::MatrixReal object then you can call sym_diagonalize on it.