Rotational equivalence of factor loading matrices with specified values

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. Here a variety of results are given for the more complex case when the specified values are not necessarily zero. A method is given for constructing reflections to preserve specified rows and columns. When the appropriatek(k – 1)/2 elements have been specified, sufficient conditions are stated for the existence of 2 ^k orthogonally equivalent matrices.This research was supported in part by the National Institute of Health Grant RR-3.