## 61 Citations

Typed Linear Algebra for Weigthed (Probabilistic) Automata

- Computer ScienceCIAA
- 2012

This paper shows typed LA at work in describing weighted (probabilistic) automata and some attention is paid to the interface between the index-free language of matrix combinators and the corresponding index-wise notation, so as to blend with traditional set theoretic notation.

Weighted Automata as Coalgebras in Categories of Matrices

- Computer ScienceInt. J. Found. Comput. Sci.
- 2013

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…

Relational style laws and constructs of linear algebra

- MathematicsJ. Log. Algebraic Methods Program.
- 2014

A linear algebra approach to OLAP

- Computer ScienceFormal Aspects of Computing
- 2014

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

- Computer Science, MathematicsDBPL
- 2017

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

- Computer ScienceJ. Log. Algebraic Methods Program.
- 2016

Compiling quantamorphisms for the IBM Q Experience

- PhysicsIEEE Transactions on Software Engineering
- 2021

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.

Calculational Proofs in Relational Graphical Linear Algebra

- MathematicsSBMF
- 2020

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

- Computer ScienceArXiv
- 2018

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).

## References

SHOWING 1-10 OF 74 REFERENCES

Matrices as Arrows!

- Computer ScienceMPC
- 2010

It is shown how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category with biproducts, which shifts the traditional view ofMatrices as indexed structures to a type-level perspective analogous to that of the pointfree algebra of programming.

Linear Algebra

- Computer Science, Mathematics
- 2008

The project before us is to introduce specialized vector-matrix notation and to extend the methods used to solve linear algebraic equations to include a full study of rank, nullity and basis from the vector-Matrix viewpoint.

Matrices, machines and behaviors

- Computer ScienceAppl. Categorical Struct.
- 1996

A bicategory whose objects are natural numbers, in which an arrow M: n→p is a finite state automaton with n input states, p output states, and some additional internal states is described, which gives a compositional semantics to a primitive notion of concurrent processes.

Do the middle letters of \OLAP" stand for Linear Algebra (\LA")?

- Computer Science
- 2011

This paper investigates, in particular, how the generation of aggregation operations such as cross tabulations and data cubes in OLAP can be expressed in terms of matrix multiplication, transposition and the Khatri-Rao variant of the Kronecker product.

Lectures on Constructive Functional Programming

- Computer Science
- 1989

This work hopes to show that a functional approach to the problem of systematically calculating programs from their specifications can take its place alongside other methodologies.

A PSEUDO REPRESENTATION THEOREM FOR VARIOUS CATEGORIES OF RELATIONS

- Mathematics
- 2000

It is well-known that, given a Dedekind category R the category of (typed) matrices with coefficients from R is a Dedekind category with arbitrary relational sums. In this paper we show that under…

Fork Algebras in Algebra, Logic and Computer Science

- Mathematics, Computer ScienceFundam. Informaticae
- 1997

This paper study fork algebras from the points of view of their algebraic and logical properties and applications, which will prove to be essential for the definition of a wide-spectrum calculus for program construction.

Encyclopedia of Parallel Computing

- Computer Science
- 2011

The highly-structured essays in this work comprise synonyms, a definition and discussion of the topic, bibliographies, and links to related literature support efficient, user-friendly searchers for immediate access to useful information.

Transforming Data by Calculation

- Computer ScienceGTTSE
- 2007

A catalog of data mappings is presented which includes abstraction and representation relations and associated constraints which are justified in an algebraic style via the pointfree-transform, a technique whereby predicates are lifted to binary relation terms in a two-level style encompassing both data and operations.