Least Squares Estimation of the Components of a Symmetric Matrix

Abstract

Y = XB + E (1) where Y and X are both s X t (s > t), of rank t, each of whose components are real and known (experimentally determined), B is the t X t symmetric flexibility matrix whose components are to be estimated and E is the matrix of discrepancies. This note exhibits the form of the symmetric matrix B. which minimizes the sum of squares of the components of E and gives a short numerical example illustrating an intuitional pitfall.