# Pairwise Axes Rotations in Factor Analysis

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A correlation matrix for eight physical variables is approximated by with , where is the diagonal matrix of the square roots of the three largest eigenvalues of and is an 8×3 matrix that contains the associated eigenvectors as columns. Using pairwise orthogonal rotations , elements of are adjusted so that the squared values in have a simple structure; that is, each row of has only one high value and the other values are relatively small in comparison. A solution approximating the results of the Varimax algorithm for orthogonal rotations (H.F. Kaiser, 1958) is given by these three rotations: -: 34° (or -56°), -: 16°, -: 20°.

Contributed by: Steve Hunka (March 2011)

Open content licensed under CC BY-NC-SA

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The eight physical variables are: (1) height, (2) arm span, (3) forearm length, (4) lower leg length, (5) weight, (6) bitrochanteric diameter, (7) chest girth, and (8) chest width. The tabular output includes the rotated matrix and the rotation matrix . Variable clusters are (1,2,3,4), (5,6,7), and (8).

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