We describe PCA mathematically as described below. Consider p random variables X 1 , X 2 , …, X p , the original system can be rotated to form a new coordinate. Let S be the covariance matrix associated with the random vector X9 = [X 1 , X 2 , …, X p ]. The corresponding eigenvalue-eigenvector pairs are (l 1 , e 1 ), (l 2 , e 2 ), …, (l p , e p ), and the ith principal component is given by: PC i~e 0 i X~e i1 X 1 ze i2 X 2 z:::ze ip X p , i~1,2,:::,p ð1Þ