On two-sided orthogonal procrustes problems

A least squares method for approximating a given symmetric matrixB by another matrixB which is orthogonally similar to a second given matrixA is derived and then generalized to nonsymmetric (but square)A andB. A possible application to ordering problems is discussed.This work was partially supported as project No. 083 by the Ohio State University, College of Education Research Grants and Leaves Program and subsequently as project I RO3 MH14097-01 by the National Institute of Mental Health. Free computer time was provided by the Ohio State University Computer Center. The writer is also pleased to record his appreciation for the time and assistance awarded to him most generously by Professors D. R. Whitney and J. S. Rustagi of the Ohio State University Mathematics Department.