On the Structure of Nonnegative Semigroups of Matrices
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The results presented here are concerned with questions of decomposability of multiplicative semigroups of matrices with nonnegative entries. Chapter 1 covers some preliminary results which become useful in the remainder of the exposition. Chapters 2 and 3 constitute an exposition of some recent known results on special semigroups. Chapter 2 explores conditions for decomposability of semigroups in terms of conditions derived from linear functionals and in Chapter 3, we give a complete proof of an extension of the celebrated Perron-Frobenius Theorem. No originality is claimed for the results in Chapters 2 and 3. In Chapter 4, we present some new results on sufficient conditions for finiteness of semigroups of matrices.
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Peter Williamson (2009). On the Structure of Nonnegative Semigroups of Matrices. UWSpace. http://hdl.handle.net/10012/4559