Kronecker Products and the Vec and Vech Operators

David A. Harville ()
Additional contact information
David A. Harville: IBM T.J. Watson Research Center, Mathematical Sciences Department

Chapter 16 in Matrix Algebra From a Statistician’s Perspective, 1997, pp 337-378 from Springer

Abstract: Abstract Some (though by no means all) of the partitioned matrices encountered in statistics are expressible in terms of two (or more) matrices (of relatively small dimensions) in the form of something called a Kronecker product. In Section 16.1, the definition of a Kronecker product of matrices is given, and a number of results on Kronecker products are presented. These results can (when applicable) be exploited for computational (and other) purposes. In subsequent sections of this chapter, the notion introduced in Chapter 15 (in connection with the differentiation of a function of a matrix) of rearranging the (nonredundant) elements of a matrix in the form of a column vector is formalized by introducing something called the vec or vech operator. A number of results on the vec or vech operator are presented. Kronecker products appear in many of these results.

Date: 1997
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-22677-4_16

Ordering information: This item can be ordered from
http://www.springer.com/9780387226774

DOI: 10.1007/0-387-22677-X_16

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().