ESS210B
Prof. Jin-Yi Yu
Determine the Projection Coefficients
qThe EOF analysis asks that the projection coefficients are determined in such a way that:
q     (1) z1 explains the maximum possible amount of the variance of the x’s;
q     (2) z2 explains the maximum possible amount of the remaining  variance
q          of the x’s;
q     (3) so forth for the remaining z’s.
q
qWith these requirements, it can be shown mathematically that the projection coefficient functions (eij) are the eigenvectors of the covariance matrix of x’s.
qThe fraction of the total variance explained by a particular eigenvector is equal to the ratio of that eigenvalue to the sum of all eigenvalues.
the orthogonal requirement in time !