Statistics Dictionary

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Matrix Transpose

The transpose of one matrix is another matrix that is obtained by using by using rows from the first matrix as columns in the second matrix.

For example, it is easy to see that the transpose of matrix A is A'. Row 1 of matrix A becomes column 1 of A'; row 2 of A becomes column 2 of A',; and row 3 of A becomes column 3 of A'.

A =    
111 222
333 444
555 666
A' =    
111 333 555
222 444 666

Note that the order of a matrix is reversed after it has been transposed. Matrix A is a 2 x 3 matrix, but matrix A' is a 3 x 2 matrix.

With respect to notation, this website uses a prime to indicate a transpose. Thus, the transpose of matrix B would be written as B'.

See also:   Types of Matrices