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ON MINIMAL SETS OF $(0,1)$-MATRICES WHOSE PAIRWISE PRODUCTS FORM A BASIS FOR $M_{n}(\mathbb{F})$

Part of: Basic linear algebra

Published online by Cambridge University Press:  28 August 2018

W. E. LONGSTAFF Open the ORCID record for W. E. LONGSTAFF [Opens in a new window]
W. E. LONGSTAFF*
Affiliation:
11 Tussock Crescent, Elanora, Queensland 4221, Australia email bill.longstaff@alumni.utoronto.ca
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Abstract

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Three families of examples are given of sets of $(0,1)$-matrices whose pairwise products form a basis for the underlying full matrix algebra. In the first two families, the elements have rank at most two and some of the products can have multiple entries. In the third example, the matrices have equal rank $\!\sqrt{n}$ and all of the pairwise products are single-entried $(0,1)$-matrices.

Keywords

matrix algebraelementary matricesbasis

MSC classification

Primary: 15A30: Algebraic systems of matrices
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 402 - 413
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Rosenthal, D., ‘Words containing a basis for the algebra of all matrices’, Linear Algebra Appl. 436 (2012), 2615–2617.Google Scholar