I store matrix entries in std::vector<double>, such that the reading is row by row. 
This means, for matrix
 1  3  4  8  9  3
 3  6  8  1  1  2
 2  0  9  8  7  6

the std::vector<double> would have entries: {1,3,4,8,9,3,3,6,8,1,1,2,2,0,9,8,7,6}. 
To transpose the matrix I use the naive approach of iterating through std::vector, calculating for each
entry its position in a matrix transpose. Recently, I got one suggestion:

"When you have a matrix and a mapping to a one-dimensional vector, transposing is equivalent to a permutation. Now execute this permutation by sorting the elements by requested rank in the permutation result." 

I understand that transposing is equivalent to a permutation, but I dont know how to approach the problem this way.
Any suggestion on how to do this (or to do matrix transpose is a faster way) is welcome.