Took a look at Math::MatrixReal Here and found the following which ran for me.

#!/usr/bin/perl -w
use Math::MatrixReal;
$matrix = Math::MatrixReal->new_from_string(<<'MATRIX');
[ 1 2 3 ]
MATRIX
# was a 3x2 matrix in original example, removed these [ 4 5 6 ]
print $matrix . "\n\n";                #added this to example
$matrix2 = Math::MatrixReal->new(3,1); #again, original was a 3x2 matr
+ix
$matrix2->transpose($matrix);
print $matrix2;
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Output:

[  1.000000000000E+00  2.000000000000E+00  3.000000000000E+00 ]


[  1.000000000000E+00 ]
[  2.000000000000E+00 ]
[  3.000000000000E+00 ]
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Hope that is helpful