Supertropical matrix algebra II: Solving tropical equations

By Zur Izhakian, Louis H. Rowen. 2009

53 citations recorded by the source corpus.

We continue the study of matrices over a supertropical algebra, proving the existence of a tangible adjoint of A, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity matrix corresponding to A; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer’s rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an n × n matrix has n distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e8bf58728024eca6ec80f243c16101af9b1aa59f

How researchers see this paper

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In Atomic and Molecular Physics, and Optics

1. Manfred Knebusch
2. Zur Izhakian
3. Louis H. Rowen

In Computational Theory and Mathematics

1. Louis H. Rowen
2. Zur Izhakian
3. Manfred Knebusch
4. Marianne Akian
5. Stephane Gaubert
6. Alexander E. Guterman

In Statistical and Nonlinear Physics

1. Manfred Knebusch
2. Zur Izhakian
3. Louis H. Rowen

Citations in the corpus

• Supertropical semirings and supervaluations (2010, background): “On the other hand, the ghost surpassing relation appears in virtually every supertropical theorem proved so far, especially in supertropical matrix theory in [IR2] and [IR3].”
• Supertropical linear algebra (2010, background): “We quote some easy properties of | gs = from [10]:”