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High-level axioms for graphical linear algebra.
- Source :
-
Science of Computer Programming . Jun2022, Vol. 218, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- • We present useful symmetrical axioms for graphical linear algebra. • We use only the diagrammatic language and its associated reasoning principles. • We develop an approach to matrices, proving its equivalence to the classical one. We focus on a modular, graphical language—graphical linear algebra—and use it as high-level language for calculational reasoning. We propose a minimal framework of axioms that highlight the dualities and symmetries of linear algebra, and showcase the resulting diagrammatic calculus. Our work develops a relational approach to linear algebra, closely connected to classical relational algebra. With the symmetrical high-level axioms we are able to provide a fully diagrammatic proof that a fragment of Graphical Linear Algebra is equivalent to matrix algebra. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR algebra
*RELATION algebras
*AXIOMS
*MATRICES (Mathematics)
*CALCULUS
Subjects
Details
- Language :
- English
- ISSN :
- 01676423
- Volume :
- 218
- Database :
- Academic Search Index
- Journal :
- Science of Computer Programming
- Publication Type :
- Academic Journal
- Accession number :
- 156452109
- Full Text :
- https://doi.org/10.1016/j.scico.2022.102791