© 2018

A Geometric Algebra Invitation to Space-Time Physics, Robotics and Molecular Geometry

  • Offers details on a state-of-art survey with the characteristics of a self-contained research monograph

  • Useful for both advanced undergraduate and graduate students with a basic background in linear algebra and geometry

  • Condenses theoretical and applied results without sacrificing quality or readability


Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Carlile Lavor, Sebastià Xambó-Descamps, Isiah Zaplana
    Pages 1-32
  3. Carlile Lavor, Sebastià Xambó-Descamps, Isiah Zaplana
    Pages 33-51
  4. Carlile Lavor, Sebastià Xambó-Descamps, Isiah Zaplana
    Pages 53-73
  5. Carlile Lavor, Sebastià Xambó-Descamps, Isiah Zaplana
    Pages 75-100
  6. Carlile Lavor, Sebastià Xambó-Descamps, Isiah Zaplana
    Pages 101-116
  7. Back Matter
    Pages 117-128

About this book


This book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. Major applications covered are the physics of space-time, including Maxwell electromagnetism and the Dirac equation; robotics, including formulations for the forward and inverse kinematics and an overview of the singularity problem for serial robots; and molecular geometry, with 3D-protein structure calculations using NMR data. The book is primarily intended for graduate students and advanced undergraduates in related fields, but can also benefit professionals in search of a pedagogical presentation of these subjects.


geometric algebra projective geometry conformal geometrical algebra Lorentz transformations Maxwell’s equations Dirac equation robot kinematics inverse kinematics molecular geometry distance geometry NMR data 3D protein structures Clifford algebra

Authors and affiliations

  1. 1.Department of Applied Maths (IMECC-UNICAMP)University of CampinasCampinasBrazil
  2. 2.Departament de MatemàtiquesUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Institut d’Org. i Control de Sist. Ind.Universitat Politècnica de CatalunyaBarcelonaSpain

About the authors

Carlile Lavor is a Full Professor at the Department of Applied Mathematics at the University of Campinas, Brazil. He holds a Ph.D. in Computer Sciences from the Federal University of Rio de Janeiro, Brazil, with post-doc studies at Duke University, USA; École Polytechnique – Paris LIX, France; and the National Laboratory for Scientific Computing (LNCC), Brazil. He co-authored the books “Introduction to Distance Geometry Applied to Molecular Geometry” and “Euclidean Distance Geometry,” and co-edited the book “Distance Geometry.” 

Sebastian Xambó-Descamps is a Full Professor of Information and Coding Theory at the Technical University of Catalonia, Spain. He holds a Ph.D. in Mathematics from the University of Barcelona, and an M.Sc. degree in Mathematics from Brandeis University, USA. He authored the books “Block Error-Correcting Codes” and “The Enumerative Theory of Conics after Halphen,” edited “Enumerative Geometry,” and co-edited "Cosmology, Quantum Vacuum and Zeta Functions," among other books. 

Isiah Zaplana graduated with a degree in Mathematics from the University of Murcia (Spain), and holds a Ph.D. in Automatic Control, Robotics and Computer Vision from the Technical University of Catalonia (Spain). He currently works in the Advanced Robotics Department of the Italian Institute of Technology as a PostDoc. His main research interest concerns to the links between robotics and mathematics.

Bibliographic information


“The present booklet is a concise presentation of main tools of geometric algebras (GAs) with selected instances of domains in which these tools are sucessfully implemented. … this brief is a very nice introduction to the subject of some important contemporary topics.” (Mircea Crâşmăreanu, zbMATH 1395.00007, 2018)

“The book under review is an abbreviated introduction to Geometric Algebra and some of its uses. … At just about 120 pages this book offers a brisk and exceling view of the many roles of Geometric Algebra.” (Jeff Ibbotson, MAA Reviews, February, 2019)