Standard Article

Kronecker Product

Statistical Theory and Methods

  1. Marc Hallin1,2

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vak004.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Hallin, M. 2013. Kronecker Product . Encyclopedia of Environmetrics.

Author Information

  1. 1

    ECARES, Université libre de Bruxelles, Bruxelles, Belgium

  2. 2

    ORFE, Princeton University, Princeton, NJ, USA

Publication History

  1. Published Online: 15 JAN 2013


The Kronecker product is a classical and an extremely convenient tool in multivariate analysis. We briefly define this product, and describe some of its main algebraic properties. We also briefly review the role of Kronecker products in the traditional assumption of separability of covariance functions in spatiotemporal models.


  • matrices;
  • vectorization;
  • trace;
  • separable covariance functions;
  • spatiotemporal models