The tropical semiring is ℝ ∪ {∞} with the operations x ⊕ y = min{x, y}, x ⊕ ∞ = ∞ ⊕ x = x, x ⊙ y = x + y, x ⊙ ∞ = ∞ ⊙ y = ∞. This paper explores how ideas from classical algebra and linear algebra over the real numbers such as polynomials, roots of polynomials, lines, matrices and matrix operations, determinants, eigen values and eigen vectors would appear in tropical mathematics. It uses numerous computed examples to illustrate these concepts and explores the relationship between certain tropical matrices and graph theory, using this to provide proofs of some tropical computations.
| Date of Award | 2015 |
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| Original language | American English |
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| Awarding Institution | - Eastern Illinois University
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| Supervisor | Peter Andrews (Supervisor) |
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- Algebra and Number Theory
A Glance at Tropical Operations and Tropical Linear Algebra
Tesfay, S. T. (Author). 2015
Student thesis: Master's Thesis › Master of Arts (MA)