1 Transposition

A matrix is transposed when the rows are written as columns and the columns are written as rows. This operation is denoted by writing ${\bf A}^{\prime}$ or ${\bf A}^{T}.$ For our example data matrix on page ,

$${\bf A}^{\prime} = \left( \begin{array}{rrrr} 50 & 100 & 150 & 200\\ 20 & 40 & 60 & 80\\ \end{array} \right)$$

a row vector is usually written

$${\bf a}^{\prime} = \left( \begin{array}{rrrr} 50 & 100 & 150 & 200\end{array} \right)$$

Clearly, $({\bf A}^{\prime})^{\prime} = {\bf A}$.