Depending why you want this, there are several different was of doing it; but since you've chosen not to answer the question; here's just one.

while( abs( $mutRate - 0.01) > 1e-16 ) {
    ++$iter;
    $k *= $mutRate * 100;

    # map $_ /= ( $mutRate * 100), @$_ for @lnPAM;
    for my $aref ( @lnPAM ) {
        $_ /= ( $mutRate * 100 ) for @$aref;
    }

    # @matrix = map[ map exp( $_ ), @$_ ], @lnPAM;
    undef @matrix;
    for my $aref ( @lnPAM ) {
        my @temp;
        push @temp, exp( $_ ) for @$aref;
        push @matrix, \@temp;
    }

    # $mutRate = sum map{ $freq[ $_ ] * ( 1 - $matrix[ $_ ][ $_ ] ) } 
+0..19;
    $mutRate = 0;
    for my $i ( 0 .. 19 ) {
        $mutRate += $freq[ $i ] * ( 1 - $matrix[ $i ][ $i ] );
    }

    printf "After %d iteration(s), k=%13.9f, RateMutation=%19.17f\n", 
+$iter, $k, $mutRate;
}
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