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}
}
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63 Citations
Highly Influential Citations
4
Background Citations
29
Methods Citations
19
Results Citations
1

63 Citations

Citation Type

Citation Type

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Weighted Automata as Coalgebras in Categories of Matrices
  • J. Oliveira
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    Int. J. Found. Comput. Sci.
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The evolution from non-deterministic to weighted automata represents a shift from qualitative to quantitative methods in computer science. The trend calls for a language able to reconcile…
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A simple inductive data type for representing correct-by-construction matrices that can be used to implement matrix-manipulation algorithms efficiently and safely, performing in some cases faster than existing alternatives even though the algorithms are written in a direct and purely functional style.
A linear algebra approach to OLAP
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This paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product.
The data cube as a typed linear algebra operator
TLDR
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
Compiling quantamorphisms for the IBM Q Experience
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
Calculational Proofs in Relational Graphical Linear Algebra
TLDR
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.
...
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