Generators, extremals and bases of max cones
... version is [7]. For more information on max algebra, its generalizations and applications the reader is referred e.g. to [2,5,8–10,16,28]. See also [20] for recent developments in the area and for further references. We give a summary of the contents of this paper. In Section 2 we begin by defining ...
... version is [7]. For more information on max algebra, its generalizations and applications the reader is referred e.g. to [2,5,8–10,16,28]. See also [20] for recent developments in the area and for further references. We give a summary of the contents of this paper. In Section 2 we begin by defining ...
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... write i 6! j if aij = 0 for every positive integer m. We say that i and j communicate and write i $ j if i ! j and j ! i. If i ! j but j 6! i for some index j , then the index i is called inessential (or transient). An index which leads to no index at all (this arises when A has a row of zeros) is a ...
... write i 6! j if aij = 0 for every positive integer m. We say that i and j communicate and write i $ j if i ! j and j ! i. If i ! j but j 6! i for some index j , then the index i is called inessential (or transient). An index which leads to no index at all (this arises when A has a row of zeros) is a ...
Homework assignments
... • Given a ring A, we write Mn (A) for the ring of n×n-matrices with entries in A, resp. GLn (A), for the group of invertible elements of the ring Mn (A). • k always stands for a (nonzero) field. Given k-vector spaces V, W, let Homk (V, W ) denote the vector space of linear maps V → W . Throughout th ...
... • Given a ring A, we write Mn (A) for the ring of n×n-matrices with entries in A, resp. GLn (A), for the group of invertible elements of the ring Mn (A). • k always stands for a (nonzero) field. Given k-vector spaces V, W, let Homk (V, W ) denote the vector space of linear maps V → W . Throughout th ...
