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- W1504902799 abstract "In this paper we generalize the max algebra system of nonnegative matrices to the class of nonnegative tensors and derive its fundamental properties. If $mathbb{A} in Re_ + ^{left[ {m,n} right]}$ is a nonnegative essentially positive tensor such that satisfies the condition class NC, we prove that there exist $mu left( mathbb{A} right)$ and a corresponding positive vector $x$ such that $mathop {max }limits_{1 le{i_2}cdots {i_m} le n} left{ {{a_{i{i_2}cdots {i_m}}}{x_{{i_2}}}cdots {x_{{i_m}}}} right}=mu left( mathbb{A} right) x_i^{m - 1},,,,,i = 1,2,cdots ,n.$ This theorem, is well known as the max algebra version of Perron--Frobenius theorem for this new system." @default.
- W1504902799 created "2016-06-24" @default.
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- W1504902799 date "2015-01-01" @default.
- W1504902799 modified "2023-09-26" @default.
- W1504902799 title "A max version of Perron--Frobenius theorem for nonnegative tensor" @default.
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- W1504902799 doi "https://doi.org/10.15352/afa/06-3-12" @default.
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