Properties of the patterned vech operator

Authors

C. A. McGilchrist, Virginia Polytechnic Institute and State University
Brian R. Cullis, Wagga Agricultural Research InstituteFollow

RIS ID

79125

Publication Details

McGilchrist, C. A. & Cullis, B. R. (1988). Properties of the patterned vech operator. Australian Journal of Statistics, 30 (1), 85-92.

Abstract

The vec operator arranges the columns of a matrix one below the other. When the matrix is symmetric such elements are not distinct but an extraction of only the distinct elements on or below the diagonal forms the operation denoted by vech. For other types of patterned matrices a ‘patterned vech’ operator is defined. The transformations from vech to vec are not uniquely defined. Here we examine properties of linear transformations which overcome the lack of uniqueness and develop properties of such linear transformations.