# THE EXISTENCE OF SOLUTION OF GENERALIZED EIGENPROBLEM IN INTERVAL MAX-PLUS ALGEBRA

### Abstract

*An eigenproblem of a matrix * * is * * where * * and * *. Vector * * and * * are eigenvector and eigenvalue, respectively. General form of eigenvalue problem is * * with * *, * *. Interval maks-plus algebra is * * and * * equipped with a maximum (* * and plus * * operations. The set of * * matrices which its component elements of * * is called matrices over interval max-plus algebra and denoted by * *. Let * *, eigenproblem in interval max-plus algebra is * * with* * and * *. Vector * * and * * are eigenvector and eigenvalue, respectively. In this research, we will discuss the generalization of the eigenproblem in interval max-plus algebra. Especially about the existence of solution of generalized eigenproblem in interval max-plus algebra. **Keywords: interval max-plus algebra, generalized eigenproblem, the existence of the solution.*

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### References

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*BAREKENG: J. Math. & App.*, vol. 17, no. 3, pp. 1341-1346, Sep. 2023.

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