Just changed the code -

$rot_mat1=eul2mat($data_doc1[$i],$data_doc1[$i+1],$data_doc1[$i+2]);  
+#Catch the reference to the first matrix 
        $rot_mat2=eul2mat($data_doc2[$i],$data_doc2[$i+1],$data_doc2[$
+i+2]);  #Catch the reference to the second matrix
        $cbn_mat=mat_multiply($rot_mat1,$rot_mat2); #Multiply the two 
+matrices
        @cbn_angles=mat2eul($cbn_mat); #Convert the matrix back to eul
+er

sub eul2mat {
        my $phi_rad=deg2rad($_[0]);
        my $theta_rad=deg2rad($_[1]);
        my $psi_rad=deg2rad($_[2]);
        #print "$phi_rad $theta_rad $psi_rad\n";
        my @rot_mat;
        $rot_mat[0][0]=cos($phi_rad)*cos($theta_rad)*cos($psi_rad)-sin
+($phi_rad)*sin($psi_rad);
        $rot_mat[0][1]=cos($phi_rad)*cos($theta_rad)*sin($psi_rad)+sin
+($phi_rad)*cos($psi_rad);
        $rot_mat[0][2]=-cos($phi_rad)*sin($theta_rad);
        $rot_mat[1][0]=-sin($phi_rad)*cos($theta_rad)*cos($psi_rad)-si
+n($psi_rad)*cos($phi_rad);
        $rot_mat[1][1]=-sin($phi_rad)*cos($theta_rad)*sin($psi_rad)+co
+s($phi_rad)*cos($psi_rad);
        $rot_mat[1][2]=sin($phi_rad)*sin($theta_rad);
        $rot_mat[2][0]=sin($theta_rad)*cos($psi_rad);
        $rot_mat[2][1]=sin($theta_rad)*sin($psi_rad);
        $rot_mat[2][2]=cos($theta_rad);
        say Dumper \@rot_mat;
        return \@rot_mat;
}

sub mat_multiply {
        my ($mat1,$mat2)=@_;
        my ($i,$j,$k);
        my $result_mat=[];
        for $i (0..2) {
                for $j (0..2) {
                        for $k (0..2) {
                                $result_mat->[$i][$j]+=$mat1->[$i][$k]
+ * $mat2->[$k][$j];
                        }
                }
        }
        return $result_mat;
}

sub mat2eul {
        print "$_[2][0]\n";
        my $theta_deg=rad2deg(atan2((sqrt($_[2][0]**2+$_[2][1]**2)),$_
+[2][2]));
        my $phi_deg=rad2deg(atan2(($_[1][2]/sin(deg2rad($theta_deg))),
+(-$_[0][2]/sin(deg2rad($theta_deg)))));
        my $psi_deg=rad2deg(atan2(($_[2][1]/sin(deg2rad($theta_deg))),
+($_[2][0]/sin(deg2rad($theta_deg)))));
        return ($theta_deg,$phi_deg,$psi_deg);
}
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I now have a bunch of uninitialized values error in the sub mat2eul. My guess is it is most probably because of the way I am accessing the values from $_. What do you think?