11. Elements of Simplicial Linear Algebra and Geometry

  1. Vera Pawlowsky-Glahn2 and
  2. Antonella Buccianti3
  1. Juan José Egozcue1,
  2. Carles Barceló-Vidal2,
  3. Josep Antoni Martín-Fernández2,
  4. Eusebi Jarauta-Bragulat1,
  5. José Luis Díaz-Barrero1 and
  6. Glòria Mateu-Figueras2

Published Online: 28 JUL 2011

DOI: 10.1002/9781119976462.ch11

Compositional Data Analysis: Theory and Applications

Compositional Data Analysis: Theory and Applications

How to Cite

Egozcue, J. J., Barceló-Vidal, C., Martín-Fernández, J. A., Jarauta-Bragulat, E., Díaz-Barrero, J. L. and Mateu-Figueras, G. (2011) Elements of Simplicial Linear Algebra and Geometry, in Compositional Data Analysis: Theory and Applications (eds V. Pawlowsky-Glahn and A. Buccianti), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119976462.ch11

Editor Information

  1. 2

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

  2. 3

    Department of Earth Sciences, University of Florence, Italy

Author Information

  1. 1

    Department of Applied Mathematics III, Technical University of Catalonia, Spain

  2. 2

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

Publication History

  1. Published Online: 28 JUL 2011
  2. Published Print: 23 SEP 2011

ISBN Information

Print ISBN: 9780470711354

Online ISBN: 9781119976462

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Keywords:

  • theory, algebra and calculus - elements of simplicial linear algebra and geometry;
  • use of simplex - as a sample space of compositional data;
  • Aitchison geometry, and development of new tools - representation of compositions;
  • elementary concepts - Euclidean character of the Aitchison geometry of the simplex;
  • linear functions, between Euclidean spaces - part of general theory, using coordinate expressions;
  • elements of simplicial geometry - n-part simplex;
  • vector space - Aitchison (1986), introducing perturbation between elements of n-part simplex;
  • centred log-ratio representation - different ways of representing a composition;
  • linear functions - simplex with perturbation, the Aitchison metrics, Euclidean space;
  • concepts of Euclidean spaces - adapted to simplex, perturbation and powering operations and Aitchison metric use

Summary

This chapter contains sections titled:

  • Introduction

  • Elements of Simplicial Geometry

  • Linear Functions

  • Conclusions

  • Acknowledgements

  • References