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

Fig. 01Source ↗

This is the original French-language artifact. I have kept it untranslated to preserve the work as it was produced.

A visual language developed within the collective ALFA project.ALFA · Hertz, Le Digabel and co-authors · CC BY 4.0

What I built

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 · Approach

I build the system, not only the asset.

01
I open with a situation or geometric question.
02
I build the model and derivation without hiding assumptions.
03
I return to interpretation, limits and computational meaning.

7 individually credited cases

The applications I explored.

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

03 · Artifacts

The reasoning, made visible.

ALFA title and co-author list including Andréa Gourion. — I am named among the co-authors on the public title page.ALFA · public title page · CC BY 4.0

Five overlapping Gershgorin discs locating matrix eigenvalues. — Eigenvalue localization without computing the eigenvalues explicitly.My case study in ALFA · CC BY 4.0

A sphere transformed into a nearly one-dimensional needle and a nearly two-dimensional disk. — Effective rank becomes visible as geometric collapse.My case study in ALFA · CC BY 4.0

04 · Observable outcome

What this project makes observable.

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.

05 · Production system

Production system

Production systemLaTeX

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.

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.

06 · Transfer

What I can transfer to another institution.

Through this work, I show how faculty collaboration, rigorous derivation, visual explanation and applied cases can live in one maintainable editorial system.

Discuss a pilot