منابع مشابه
A Combinatorial Approach to Matrix Algebra
To most contemporary mathematicians matrices and linear transformations are practically interchangeable notions . Indeed, the mainstream 'Bourbakian' establishment, with its profound disdain of the concrete, goes as far as to frown at the mere mention of the word 'matrix'. To me, however, (as well as to a growing number of mathematical dissidents c~lled 'combinatorialists') a matrix has nothing...
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In this paper we investigate eigenvalues of matrix representations of trees as a means by which one might quantify the shape of a tree. We consider the adjacency matrix, the Laplacian matrix, and the pairwise distance matrix of the tree. We then demonstrate that for any of these choices of matrix the fraction of trees with a unique set of eigenvalues goes to zero as the number of leaves goes to...
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The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operatorvalued free probability. The paper presents constructions for maps with similar properties to the H and K transforms from the literature, semi inner-product bimodule analogues for the monotone and weakly monotone product of Hilbert spaces, an ad-hoc versio...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1985
ISSN: 0012-365X
DOI: 10.1016/0012-365x(85)90192-x