The purpose of this class is to understand the fundamental properties of max-plus algebra and its relationship with graph
theory, as well as eigenvalues and eigenvectors in max-plus algebra and their applications.
Max-plus (or min-plus) algebra is an algebraic structure known as an idempotent semiring. It has diverse origins in applications
and has developed independently within various applied fields. In recent years, an area of mathematics known as tropical geometry
has been actively studied. Tropical geometry can be regarded as algebraic geometry over the max-plus algebra.
On the other hand, many properties and theorems well known in classical linear algebra are known to have analogous counterparts in max-plus algebra, and this area is sometimes referred to as tropical linear algebra.
In this course, we will study the fundamental properties of max-plus algebra and its connections with graph theory, and we will also discuss eigenvalues and eigenvectors in max-plus algebra and their applications.
On the other hand, many properties and theorems well known in classical linear algebra are known to have analogous counterparts in max-plus algebra, and this area is sometimes referred to as tropical linear algebra.
In this course, we will study the fundamental properties of max-plus algebra and its connections with graph theory, and we will also discuss eigenvalues and eigenvectors in max-plus algebra and their applications.
- Students can understand the definition and basic properties of max-plus algebra
- Students can understand linear algebra over max-plus algebra, properties of eigenvalues and eigenvectors, and their applications.
- Students can understand the mim-plus analogy of the qd algorithm
| report | Total. | |
|---|---|---|
| 1. | 40% | 40% |
| 2. | 40% | 40% |
| 3. | 20% | 20% |
| Total. | 100% | - |
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | Guidance Definition of max-plus algebra, basic properties |
Review of linear algebra | 190minutes |
| 2． | Polynomials and factorizations on max-plus algebra | Review of previous classes | 190minutes |
| 3． | Functions on max-plus algebras and their graphs | Review of previous classes | 190minutes |
| 4． | Linear algebra over max-plus algebras | Review of previous classes | 190minutes |
| 5． | Matrices over max-plus algebra and graphs | Review of previous classes | 190minutes |
| 6． | Eigenvalues and eigenvectors over max-plus algebra, and graphs | Review of previous classes | 190minutes |
| 7． | Min-plus analogy of the qd algorithm | Review of previous classes | 190minutes |
| 8． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 9． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 10． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 11． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 12． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 13． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 14． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| Total. | - | - | 1330minutes |
Evaluation will be based on a short report on each lecture and a final report at the end of the term.
A student will pass the course if he/she is judged to have understood at least 60% of the content of the lectures.
A student will pass the course if he/she is judged to have understood at least 60% of the content of the lectures.
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
Basic knowledge of linear algebra I/II, numerical analysis I/II, and algebra is preferred.
- Tuesday, 4th period; if you have any questions, it is preferable to make an appointment in advance by email.
- Course that cultivates a basic problem-solving skills
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Sat Mar 14 14:33:28 JST 2026