Typing linear algebra: A biproduct-oriented approach

@article{Macedo2013TypingLA,
  title={Typing linear algebra: A biproduct-oriented approach},
  author={Hugo Daniel Macedo and Jos{\'e} Nuno Oliveira},
  journal={ArXiv},
  year={2013},
  volume={abs/1312.4818}
}
View PDF on arXiv
61 Citations
Highly Influential Citations
4
Background Citations
29
Methods Citations
17
Results Citations
1

61 Citations

Citation Type

Citation Type

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The data cube as a typed linear algebra operator
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This paper shows that a typed notation for linear algebra exists and can be useful in formalizing and reasoning about data aggregation operations, and one such operation - the construction of a data cube - is shown to be easily expressible as a linear algebra operator.
Gaussian elimination is not optimal, revisited
  • H. D. Macedo
  • Computer Science
    J. Log. Algebraic Methods Program.
  • 2016
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TLDR
This paper aims at building correct-by-construction quantum circuits to be deployed on quantum devices such as those available at the IBM Q Experience, to contribute to extending the laws of classical program algebra to quantum programming.
Relations in linear algebra
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This work proposes a minimal framework of six axioms that highlight the dualities and symmetries of linear algebra, and uses the resulting diagrammatic calculus as a convenient tool to prove a number of diverse theorems.
Typed Linear Algebra for Efficient Analytical Querying
TLDR
This paper uses typed linear algebra to represent data and perform analytical querying in a single, unified framework and compares the performance of the LA-based approach with popular database competitors (PostgreSQL and MySQL).
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