Memory efficient transpose - Awk

Here's one way to do it, as I mentioned in my comments, in chunks. Here I show the mechanics on a tiny 12r x 10c file, but I also ran a chunk of 1000 rows on a 10K x 10K file in not much more than a minute (Mac Powerbook).6

EDIT The following was updated to consider an M x N matrix with unequal number of rows and columns. The previous version only worked for an 'N x N' matrix.

$ cat et.awk
BEGIN {
    start = chunk_start
    limit = chunk_start + chunk_size - 1
}

{
    n = (limit > NF) ? NF : limit
    for (f = start; f <= n; f++) {
        a[NR, f] = $f
    }
}

END {
    n = (limit > NF) ? NF : limit

    for (f = start; f <= n; f++)
      for (r = 1; r <= NR; r++)
        printf a[r, f] (r==NR ? RS : FS)
}


$ cat t.txt
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 
30 31 32 33 34 35 36 37 38 39 
40 41 42 43 44 45 46 47 48 49 
50 51 52 53 54 55 56 57 58 59 
60 61 62 63 64 65 66 67 68 69 
70 71 72 73 74 75 76 77 78 79 
80 81 82 83 84 85 86 87 88 89 
90 91 92 93 94 95 96 97 98 99 
A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 
B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 


$ cat et.sh
inf=$1
outf=$2

rm -f $outf
for i in $(seq 1 2 12); do
    echo chunk for rows $i $(expr $i + 1)
    awk -v chunk_start=$i -v chunk_size=2 -f et.awk $inf >> $outf
done



$ sh et.sh t.txt t-transpose.txt
chunk for rows 1 2
chunk for rows 3 4
chunk for rows 5 6
chunk for rows 7 8
chunk for rows 9 10
chunk for rows 11 12


$ cat t-transpose.txt 
10 20 30 40 50 60 70 80 90 A0 B0 C0
11 21 31 41 51 61 71 81 91 A1 B1 C1
12 22 32 42 52 62 72 82 92 A2 B2 C2
13 23 33 43 53 63 73 83 93 A3 B3 C3
14 24 34 44 54 64 74 84 94 A4 B4 C4
15 25 35 45 55 65 75 85 95 A5 B5 C5
16 26 36 46 56 66 76 86 96 A6 B6 C6
17 27 37 47 57 67 77 87 97 A7 B7 C7
18 28 38 48 58 68 78 88 98 A8 B8 C8
19 29 39 49 59 69 79 89 99 A9 B9 C9

And then running the first chunk on the huge file looks like:

$ time awk -v chunk_start=1 -v chunk_size=1000 -f et.awk tenk.txt  > tenk-transpose.txt

real    1m7.899s
user    1m5.173s
sys     0m2.552s

Doing that ten times with the next chunk_start set to 1001, etc. (and appending with >> to the output, of course) should finally give you the full transposed result.