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Rotation of Axes

In both principal component analysis and factor analysis, it is sometimes desirable to perform a linear transformation of the original components or factors. This operation is performed to arrive at simple structure where the coefficients of the vectors related to these new transformed variables are either as large as possible or close to zero. These new coefficients may be used either to aid in the interpretation of the original components or factors, or to cluster the original variables. This linear transformation amounts to a rotation of the axes related to the components or factors. The rotation may be orthogonal in which case the resultant new set of vectors are still at right angles to each other or oblique in which they are not. Loss of orthogonality may result in better interpretation of the original vector sets or clustering of the original variables. Several numerical examples are given to illustrate these procedures including one where rotation is not appropriate. 
 
 
Keywords: 
 
principal component analysis; 
factor analysis; 
rotation; 
simple structure