Graphical Representation of Asymmetric Matrices

Summary When sample units are plotted against orthogonal principal axes in a components analysis, the concept of (Euclidean) distance plays a central point in interpretation. Variants of such diagrams are common throughout multivariate analysis. Because distance between a pair of points is independent of the order in which they are taken, displays of this kind are especially associated with symmetric matrices, but methods are also required for displaying asymmetric matrices. In this paper two methods for displaying asymmetric square matrices are presented and illustrated by examples. In the first method (multidimensional unfolding) the square matrix is regarded as part of an otherwise unknown symmetric matrix and the resulting diagram is interpreted using distances, much as with classical methods. In the second method the matrix is partitioned into its symmetric and skew‐symmetric components. While the symmetric part is represented by some established distance‐based method, the skew‐symmetric part is represented by points whose relationships are interpreted in terms of areas of triangles and co‐linearities.