I think dummy dimensions add only a few bytes to PDL-struct header, but your approach really physicalizes arrays from 2D to 4D (edit: well, it's still same 2D but squared dimensions for this example, sorry), which has grave consequences for performance. If no-one ever needs Kronecker product of 80x80 matrices, then count this comment as another nitpick :). + Note report of memory consumption assumes Win32, so disable/replace otherwise.

use strict;
use warnings;
use feature 'say';
use PDL;
use Time::HiRes 'time';

use constant DIM => 80;
my $x = random DIM, DIM;
my $y = random DIM, DIM;

report( 'choroba, vr', \&kronecker_product, $x, $y );
report( 'etj', \&kron, $x, $y );

sub report {
    my ( $monk, $code, $x, $y ) = @_;
    
    my $t = time;
    my $k = $code-> ( $x, $y );
    say "$monk:";
    say 'time: ', time - $t; 
    say 'memory: ', mem();
}

sub mem {
    qx{ typeperf "\\Process(perl)\\Working Set Peak" -sc 1 } 
        =~ /(\d+)\.\d+\"$/m;
    ( my $s = $1 ) =~ s/(\d{1,3}?)(?=(\d{3})+$)/$1,/g;
    return $s
}

sub kronecker_product {
    use PDL::NiceSlice;
    my ( $x, $y ) = @_;

    ( $x( *1, *1 ) * $y )
        -> clump( 0, 2 )
        -> clump( 1, 2 )
}

sub PDL::dupN {
  my ($this, @times) = @_;
  return $this->copy if !grep $_ != 1, @times;
  my $sl = join ',', map ":,*$_", @times;
  $this = $this->slice($sl);
  $this = $this->clump($_, $_+1) for 0..$#times;
  $this;
}

sub PDL::inflateN {
  my ($this, @times) = @_;
  return $this->copy if !grep $_ != 1, @times;
  my $sl = join ',', map "*$_,:", @times;
  $this = $this->slice($sl);
  $this = $this->clump($_, $_+1) for 0..$#times;
  $this;
}

sub kron { my ($x,$y) = @_; $x->inflateN($y->dims) * $y->dupN($x->dims
+) }

__END__

choroba, vr:
time: 0.0958220958709717
memory: 355,741,696
etj:
time: 8.45677018165588
memory: 2,977,234,944
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Edit 2. By the way, while we are at this example, the PDL::NiceSlice says

• arguments should not be quoted
• lone '*' inserts a dummy dimension of order 1

but I see that lone unquoted star(s) cause Perl to produce a warning:

Use of uninitialized value in concatenation (.) or string

so I had to insert a pair of very unsightly "1"'s, which of course devalues code nicety by half at least:). Is this a bug in PDL::NiceSlice, documentation flaw, or just me reading it incorrectly?