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 appropriate k ( k − 1)/2 elements have been specified, sufficient conditions are stated for the existence of 2 k orthogonally equivalent matrices.