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Minimax Algebra

  • Book
  • © 1979

Overview

Authors:
  1. Raymond Cuninghame-Green

    1. Dept. of Mathematical Statistics, University of Birmingham, Birmingham, England

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 166)

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Table of contents (29 chapters)

  1. Front Matter

    Pages N2-XI
    Download chapter PDF

  2. Motivation

    • Raymond Cuninghame-Green
    Pages 1-10

  3. The Initial Axioms

    • Raymond Cuninghame-Green
    Pages 11-24

  4. Opening and Closing

    • Raymond Cuninghame-Green
    Pages 25-32

  5. The Principal Interpretation

    • Raymond Cuninghame-Green
    Pages 33-39

  6. The Spaces En and ℳmn

    • Raymond Cuninghame-Green
    Pages 40-51

  7. Duality for Matrices

    • Raymond Cuninghame-Green
    Pages 52-55

  8. Conjugacy

    • Raymond Cuninghame-Green
    Pages 56-61

  9. AA* Relations

    • Raymond Cuninghame-Green
    Pages 62-71

  10. Some Schedule Algebra

    • Raymond Cuninghame-Green
    Pages 72-76

  11. Residuation and Representation

    • Raymond Cuninghame-Green
    Pages 77-85

  12. Trisections

    • Raymond Cuninghame-Green
    Pages 86-92

  13. σø-Astic Matrices

    • Raymond Cuninghame-Green
    Pages 93-99

  14. /-Existence

    • Raymond Cuninghame-Green
    Pages 100-111

  15. The Equation A ⊗ x = b Over a Blog

    • Raymond Cuninghame-Green
    Pages 112-118

  16. Linear Equations Over a Linear Blog

    • Raymond Cuninghame-Green
    Pages 119-129

  17. Linear Dependence

    • Raymond Cuninghame-Green
    Pages 130-140

  18. Rank of Matrices

    • Raymond Cuninghame-Green
    Pages 141-146

  19. Seminorms on En

    • Raymond Cuninghame-Green
    Pages 147-153

  20. Some Matrix Spaces

    • Raymond Cuninghame-Green
    Pages 154-161
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Keywords

About this book

A number of different problems of interest to the operational researcher and the mathematical economist - for example, certain problems of optimization on graphs and networks, of machine-scheduling, of convex analysis and of approx­ imation theory - can be formulated in a convenient way using the algebraic structure (R,$,@) where we may think of R as the (extended) real-number system with the binary combining operations x$y, x®y defined to be max(x,y),(x+y) respectively. The use of this algebraic structure gives these problems the character of problems of linear algebra, or linear operator theory. This fact hB.s been independently discovered by a number of people working in various fields and in different notations, and the starting-point for the present Lecture Notes was the writer's persuasion that the time had arrived to present a unified account of the algebra of linear transformations of spaces of n-tuples over (R,$,®),to demonstrate its relevance to operational research and to give solutions to the standard linear-algebraic problems which arise - e.g. the solution of linear equations exactly or approximately, the eigenvector­ eigenvalue problem andso on.Some of this material contains results of hitherto unpublished research carried out by the writer during the years 1970-1977.

Authors and Affiliations

  • Dept. of Mathematical Statistics, University of Birmingham, Birmingham, England

    Raymond Cuninghame-Green

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