• Corpus ID: 238253264

Independence and orthogonality of algebraic eigenvectors over the max-plus algebra

@inproceedings{Nishida2021IndependenceAO,
  title={Independence and orthogonality of algebraic eigenvectors over the max-plus algebra},
  author={Yuki Nishida and Sennosuke Watanabe and Yoshihide Watanabe},
  year={2021}
}
The max-plus algebra R ∪ {−∞} is a semiring with the two operations: addition a ⊕ b := max(a, b) and multiplication a ⊗ b := a + b. Roots of the characteristic polynomial of a max-plus matrix are called algebraic eigenvalues. Recently, algebraic eigenvectors with respect to algebraic eigenvalues were introduced as a generalized concept of eigenvectors. In this paper, we present properties of algebraic eigenvectors analogous to those of eigenvectors in the conventional linear algebra. First, we… 

Figures from this paper

References

SHOWING 1-10 OF 33 REFERENCES

On The Vectors Associated with the Roots of Max-Plus Characteristic Polynomials

The notion of algebraic eigenvectors associated with the roots of characteristic polynomials is given and the eigenvalue problem in the max-plus algebra is discussed.

A min-plus analogue of the Jordan canonical form associated with the basis of the generalized eigenspace

ABSTRACT In this paper, we investigate a min-plus analogue of Jordan canonical forms of matrices. We first define the generalized eigenvector of a min-plus matrix A as an eigenvector of the kth power

Supertropical matrix algebra II: Solving tropical equations

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

Supertropical matrix algebra

AbstractThe objective of this paper is to develop a general algebraic theory of supertropical matrix algebra, extending [11]. Our main results are as follows: The tropical determinant (i.e.,

Linear independence over tropical semirings and beyond

The symmetrization of the max-plus algebra is revisited, establishing properties of linear spaces, linear systems, and matrices over the symmetrized max- plus algebra and developing some general technique to prove combinatorial and polynomial identities for matricesover semirings.

Supertropical algebra

Dependence of supertropical eigenspaces

ABSTRACT We study the pathology that causes tropical eigenspaces of distinct supertropical eigenvalues of a nonsingular matrix A, to be dependent. We show that in lower dimensions the eigenvectors of

Max-linear Systems: Theory and Algorithms

Max-algebra: Two Special Features.- One-sided Max-linear Systems and Max-algebraic Subspaces.- Eigenvalues and Eigenvectors.- Maxpolynomials. The Characteristic Maxpolynomial.- Linear Independence

Reducible Spectral Theory with Applications to the Robustness of Matrices in Max-Algebra

First, a complete account of the reducible max-algebraic spectral theory is given, and then it is applied to characterize robust matrices.