Relational style laws and constructs of linear algebra

  • We present a few laws of linear algebra inspired by laws of relation algebra. The linear algebra laws are obtained from the relational ones by replacing union, intersection, composition and converse by the linear algebra operators of addition, Hadamard product, composition and transposition. Many of the modified expressions hold directly or with minor alterations. We also define operators that sum up the content of rows and columns. These share many properties with the relational domain and codomain operators returning a subidentity corresponding to the domain and codomain of a relation. Finally, we use the linear algebra operators to write axioms defining direct sums and direct products and we show that there are other solutions in addition to the traditional – in the relational context – injection and projection relations.

Download full text files

Export metadata


Number of document requests

Additional Services

Share in Twitter Search Google Scholar
Author:Jules Desharnais, Anastasiya Grinenko, Bernhard MöllerGND
Frontdoor URL
Parent Title (English):Journal of Logical and Algebraic Methods in Programming
Publisher:Elsevier BV
Year of first Publication:2014
Publishing Institution:Universität Augsburg
Release Date:2019/07/23
First Page:154
Last Page:168
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand)