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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/101594

    Title: Nonnegative square roots of nonnegative matrices
    Other Titles: 非負矩陣之非負平方根
    Authors: 黃鵬瑞;Huang, Peng-Rui
    Contributors: 淡江大學數學學系碩士班
    譚必信;Tam, Bit-Shun
    Keywords: 非負矩陣;非負平方根;Nonnegative matrix;nonnegative square root;Perron-Frobenius theorem;square root of digraph
    Date: 2014
    Issue Date: 2015-05-01 16:11:18 (UTC+8)
    Abstract: 一般方陣的平方根問題,在許多現有的文獻中已經可以找到答案。
    For a complex square matrix, there are many references on the question of the existence of a square root. However, not much is known about the question of existence of entrywise nonnegative square roots for an entrywise square nonnegative matrix. The purpose of this thesis is to address the question of when a nonnegative matrix has a nonnegative square root. We settle the existence and uniqueness question for $2 times 2$ nonnegative matrices. We relate the nonnegative square root problem for nonnegative matrices to the square root problem for digraphs, and focus on nonnegative matrices whose digraphs are paths, circuits, permutation digraphs or bigraphs. Moreover, we characterize rank-one nonnegative matrices that have nonnegative $p$th root, and nonnegative square roots of nonnegative monomial matrices, and also treat the question of when a symmetric nonnegative matrix has a symmetric nonnegative square root.
    Appears in Collections:[數學學系暨研究所] 學位論文

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