The transpose operator, denoted by the backquote character (`), exchanges the rows and columns of matrix, producing the transpose of matrix. If is the value in the th row and th column of matrix, then the transpose of matrix contains in the th row and th column. If matrix contains rows and columns, the transpose has rows and columns.

For example, the following statements transpose the matrix a, shown in Figure 23.29:

a = {1 2,
     3 4,
     5 6};
b = a`;
print b;

You can also transpose a matrix with the T function.