Statistical interpretation of matrices

The vector of column-means m of an nxp matrix X is defined as follows  

The elements of are the coordinates of the column-centroid. Geometrically, this 

In order to be consistent with the concept of the two dual data spaces, we must also define the vector of row-means 

The elements of m represent the coordinates of the row-centroid, which corresponds with the center of mass of the column-pattern P of points formed in 

Usually, the raw data in a matrix are preprocessed before being submitted to multivariate analysis. A common operation is reduction by the mean or centering. Centering is a standard transformation of the data which is applied in principal components analysis (Section 31.3). Subtraction of the column-means from the elements in the corresponding columns of an nxp matrix X produces the matrix of 

---