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| q |
The EOF analysis asks that the projection coefficients are
determined in
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such a way that:
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(1) z1
explains the maximum possible amount of the variance of the x’s;
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(2) z2
explains the maximum possible amount of the remaining variance
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of the x’s;
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(3) so forth for the
remaining z’s.
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With these requirements, it can be shown mathematically that the
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projection coefficient functions (eij)
are the eigenvectors of the covariance
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matrix of x’s.
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The fraction of the total variance explained by a
particular eigenvector is
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equal to the ratio of that eigenvalue to the sum of all eigenvalues.
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