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Open textbook · Co-author · 7 individually credited cases

ALFA · Applied cases across linear algebra

Move from phenomenon, to model, to algebra, to interpretation.

Role
Co-author; individually credited case-study author
Period
Since May 2025
Status
Public collective work · CC BY 4.0 unless noted otherwise
Discipline
Applied linear algebra · collective open textbook

Complex roots · ALFA

Fig. 01

A visual language developed within the collective ALFA project.

FR originalFive complex fifth roots arranged as a regular pentagon in the complex plane.
Source ALFA · Hertz, Le Digabel and co-authors · CC BY 4.0
What I produced
  • Seven individually credited case studies
  • Applications spanning interpolation, spectra, dynamics and SVD
  • Contributions inside a collective editorial system
Open the public ALFA PDF
Production systemLaTeX

01 · Context + problem

The design challenge

I have contributed to ALFA as a co-author since May 2025. This open, collaborative French-language resource is led by Alain Hertz and Sébastien Le Digabel.

Applied linear algebra has to preserve rigor while showing why the abstraction matters in computation, geometry and dynamical systems.

02 · Constraints

What the project had to respect.

  • Keep collective authorship explicit
  • Credit only seven studies individually to Andréa
  • Retain version and CC BY 4.0 caveat
What was produced
  • Seven individually credited case studies
  • Applications spanning interpolation, spectra, dynamics and SVD
  • Contributions inside a collective editorial system

03 · How it was built

How I built the content.

  1. 01

    I open with a situation or geometric question.

  2. 02

    I build the model and derivation without hiding assumptions.

  3. 03

    I return to interpretation, limits and computational meaning.

7 individually credited cases

The applications I explored.

  1. 01Inverse d’une matrice 2 × 2 par blocs
  2. 02Polynômes de Lagrange
  3. 03De la corde pincée au spectre des opérateurs
  4. 04Algorithme des puissances itérées
  5. 05Stabilité de systèmes dynamiques
  6. 06Théorème de Gerschgorin
  7. 07Rang effectif d’une matrice

05 · Work and scope

What this work shows.

Materials produced

  • Public edition consulted on 26 August 2026; new releases are published frequently
  • Seven sections explicitly signed “par Andréa Gourion”
  • Book credits naming project leads, co-authors and licence

Scope of this presentation

ALFA is a collective work. My individual contribution is identified by the signature on each of my seven studies.

The presentation concerns published contributions, without a study of their effect on learning.

Open the current ALFA PDF

Visible results

  • Seven named studies integrated into the book
  • A span from block matrices to effective rank
  • Visual bridges between complex arithmetic and geometry
Limits and status

ALFA is collective. I credit the complex-number figures to the project and do not claim them as my exclusive work.

06 · Relevance for your organisation

What this approach makes possible.

Within a collective publication, I can take responsibility for writing an applied case and producing its figures. Your team retains editorial and pedagogical direction. We agree on attribution, review, formats and the files delivered for that contribution.

Is your team preparing similar content?

Explore the eight-week pilot Ask me a question

07 · Production system

Production system

Production systemLaTeX
01

Collective mathematical production

ALFA is composed as one long-form mathematical work rather than assembled from disconnected page files.

LaTeX

Why it mattersNotation, navigation and references can remain coherent across a large collaborative resource.

02

Study-level attribution

The collective document explicitly identifies the seven case studies credited to Andréa while preserving the book’s shared authorship.

LaTeX

Why it mattersReaders can distinguish individual evidence from the collective production without overstating authorship.