Matrix Multiplication, Three Arithmetics
Tropical algebra
Linear algebra
Min-plus
Click any entry of a matrix product and see its candidates — under ordinary, min-plus, and max-plus arithmetic.
Explainers
Educational HTML artifacts and visual explainers.
Each artifact here is a self-contained static page that works offline and is independently archivable — a landing page explains the idea, and a full-screen explorer runs the interactive application. Some explainers form a series that reads in order (each page carries Previous/Next links); others stand alone. Filter by topic using the tags in the sidebar.
Start here
The first series builds from the arithmetic up — begin with how the product of two matrices changes when you swap the arithmetic:
Matrix Multiplication, Three Arithmetics
Click any entry of a matrix product and watch its candidates resolve — under ordinary, min-plus, and max-plus arithmetic. One winning term becomes a witness: the cheapest stop, or the binding constraint. It’s the foundation the rest of the series builds on.
Series: Tropical Algebra
A five-part mini-course tracing a single idea — replacing ordinary addition with min or max — from arithmetic, to algorithms, to hardware, to cycles. Read in order:
- Matrix Multiplication, Three Arithmetics — what a matrix product means under ordinary, min-plus, and max-plus arithmetic.
- Shortest Paths as Relaxation Schedules — the same min-plus product, now as the classic shortest-path algorithms.
- All-Pairs Distances by Admitting Intermediates — the same min-plus update, now filling the whole distance matrix: Floyd–Warshall as the
O(n³)route to the closureW*. - Inside a Tropical GEMM Kernel — how that product actually runs on hardware: an add-and-compare with no FMA.
- Cyclic Schedules and the Max-Plus Eigenvalue — close the schedule into a loop and read its long-run beat as an eigenvalue.
The cards below are in the same order; each page also carries Previous/Next links.
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