my @matrix = (
    [ qw( 1  2  4  4 ) ],
    [ qw( 5  2  0  8 ) ],
    [ qw( 9 10 11 12 ) ],
); 

my @t;
foreach my $column_num ( 0 .. $#{ $matrix[0] } ) {
    my @slice = map { $_->[$column_num] } @matrix;
    
    my @r;
    foreach my $n ( @slice ) {
        last if $n == 0;
        push @r, $n;
    }
    
    push @t, [@r];
}