International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 411-415

Computations for a vibrating system diagonalize the variance

J. N. Boyd and P. N. Raychowdhury

Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284-2014, Virginia, USA

Received 11 August 1993; Revised 15 September 1993

Copyright © 1995 J. N. Boyd and P. N. Raychowdhury. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The transformations to diagonalize potential energy matrices for coupled harmonic oscillators will also diagonalize the variance when written in matrix form. After a brief review of a geometrical interpretation of the variance, the transformations are described and an example is given.