Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The direct product permuting matrices

Holmquist, Björn LU orcid (1985) In Linear and Multilinear Algebra 17(2). p.117-141
Abstract
A new matrix product is defined and its properties are investigated. The commutatuion matrix which flips a left direct product of two matrices into a right direct one is derived as a composition of two identity matrices. The communication matrix is a special case of the direct product permuting matrices defined in this paper which are matrix representations of the permutation operators on tensor spaces i e. the linear mappings which permute the order of the vectors in a direct product of them. Explicit expressions for these matrices are given. properties of the matrices are investigated and it is shown how these matrices, act on various representations of tensor spaces.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Linear and Multilinear Algebra
volume
17
issue
2
pages
117 - 141
publisher
Taylor & Francis
external identifiers
  • scopus:26844523611
ISSN
1026-7573
DOI
10.1080/03081088508817648
language
English
LU publication?
yes
id
963801d0-91d9-4e19-b0e6-f3218795877d (old id 4934142)
date added to LUP
2016-04-01 12:06:59
date last changed
2025-04-04 14:46:46
@article{963801d0-91d9-4e19-b0e6-f3218795877d,
  abstract     = {{A new matrix product is defined and its properties are investigated. The commutatuion matrix which flips a left direct product of two matrices into a right direct one is derived as a composition of two identity matrices. The communication matrix is a special case of the direct product permuting matrices defined in this paper which are matrix representations of the permutation operators on tensor spaces i e. the linear mappings which permute the order of the vectors in a direct product of them. Explicit expressions for these matrices are given. properties of the matrices are investigated and it is shown how these matrices, act on various representations of tensor spaces.}},
  author       = {{Holmquist, Björn}},
  issn         = {{1026-7573}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{117--141}},
  publisher    = {{Taylor & Francis}},
  series       = {{Linear and Multilinear Algebra}},
  title        = {{The direct product permuting matrices}},
  url          = {{http://dx.doi.org/10.1080/03081088508817648}},
  doi          = {{10.1080/03081088508817648}},
  volume       = {{17}},
  year         = {{1985}},
}