Pairwise Axes Rotations in Factor Analysis

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°.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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).
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+