Coefficients alpha and reliabilities of unrotated and rotated components

It has been shown by Kaiser that the sum of coefficients alpha of a set of principal components does not change when the components are transformed by an orthogonal rotation. In this paper, Kaiser's result is generalized. Fir st, the invariance property is shown to hold for any set of orthogonal comp onents. Next, a similar invariance property is derived for the reliability of any set of components. Both generalizations are established by consideri ng simultaneously optimal weights for components with maximum alpha and wit h maximum reliability, respectively. A short-cut formula is offered to eval uate the coefficients alpha for orthogonally rotated principal components f rom rotation weights and eigenvalues of the correlation matrix. Finally, th e greatest lower bound to reliability and a weighted version are discussed.