On constructing nearly decomposable matrices
نویسندگان
چکیده
منابع مشابه
r-Indecomposable and r-Nearly Decomposable Matrices
Let n, r be integers with 0 ≤ r ≤ n− 1. An n×n matrix A is called r-partly decomposable if it contains a k×l zero submatrix with k+l = n−r+1. A matrix which is not r-partly decomposable is called r-indecomposable (shortly, r-inde). Let Eij be the n × n matrix with a 1 in the (i, j) position and 0’s elsewhere. If A is r-indecomposable and, for each aij 6= 0, the matrix ∗Research supported by Nat...
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Recently, some techniques such as adding whiskers and attaching graphs to vertices of a given graph, have been proposed for constructing a new vertex decomposable graph. In this paper, we present a new method for constructing vertex decomposable graphs. Then we use this construction to generalize the result due to Cook and Nagel.
متن کاملconstructing vertex decomposable graphs
recently, some techniques such as adding whiskers and attaching graphs to vertices of a given graph, have been proposed for constructing a new vertex decomposable graph. in this paper, we present a new method for constructing vertex decomposable graphs. then we use this construction to generalize the result due to cook and nagel.
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In this paper, it is shown that nearly completely decomposable (NCD) Markov chains are quasi{lumpable. The state space partition is the natural one, and the technique may be used to compute lower and upper bounds on the stationary probability of each NCD block. In doing so, a lower bounding nonnegative coupling matrix is employed. The nature of the stationary probability bounds is closely relat...
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Nearly positive matrices are nonnegative matrices which, when premultiplied by orthogonal matrices as close to the identity as one wishes, become positive. In other words, all columns of a nearly positive matrix are mapped simultaneously to the interior of the nonnegative cone by mutiplication by a sequence of orthogonal matrices converging to the identity. In this paper, nearly positive matric...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0268062-4