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• W1966527240 abstract "In this paper we study the positive definiteness of meet and join matrices using a novel approach. When the set $S_n$ is meet closed, we give a sufficient and necessary condition for the positive definiteness of the matrix $(S_n)_f$. From this condition we obtain some sufficient conditions for positive definiteness as corollaries. We also use graph theory and show that by making some graph theoretic assumptions on the set $S_n$ we are able to reduce the assumptions on the function $f$ while still preserving the positive definiteness of the matrix $(S_n)_f$. Dual theorems of these results for join matrices are also presented. As examples we consider the so-called power GCD and power LCM matrices as well as MIN and MAX matrices. Finally we give bounds for the eigenvalues of meet and join matrices in cases when the function $f$ possesses certain monotonic behaviour." @default.
• W1966527240 created "2016-06-24" @default.
• W1966527240 creator A5020763154 @default.
• W1966527240 creator A5049044996 @default.
• W1966527240 date "2012-09-19" @default.
• W1966527240 modified "2023-09-27" @default.
• W1966527240 title "On the positive definiteness and eigenvalues of meet and join matrices" @default.
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• W1966527240 hasPublicationYear "2012" @default.
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