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Abstract
Abstract-This paper discusses the Cholesky decomposition in the symmetrized max-plus algebra. By using a link between the conventional algebra and the symmetrized max-plus algebra, we show the existence of the Cholesky decomposition of a matrix over the symmetrized max-plus algebra. A matrix has the Cholesky decomposition if it is symmetric and has principal leading submatrices whose determinant are positive. The results can be used to determine the solution of linear balance systems.
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1 assistant professor in Departement of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Jenderal Soedirman, Jl. Dr. Soeparno 61 Karangwangkal, Purwokerto Utara, Banyumas, 53123, Central Java, Indonesia
2 associate Professor in Departement of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Bulaksumur 55281, Sleman, Yogyakarta, Indonesia
3 associate professor in Departement of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Bulaksumur 55281, Sleman, Yogyakarta, Indonesia Yogyakarta, Indonesia