Abstract
We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes. For an incomparable pair (X1,X2) of classes of matrices with variants of the diagonal dominance property, we also study the problem of providing sufficient conditions for the matrices in Xi to be in Xj with {i,j}={1,2}. The article is a continuation of a series of articles on the topic and related topics by the author; see [1][2][3][4].
Highlights
Introduction and NotationThe theory of matrices with variants of the diagonal dominance property has attracted the attention of researchers in matrix analysis and its applications
We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes
For an incomparable pair ( X1, X 2 ) of classes of matrices with variants of the diagonal dominance property, we study the problem of providing sufficient conditions for the matrices in Xi to be in
Summary
The theory of matrices with variants of the diagonal dominance property has attracted the attention of researchers in matrix analysis and its applications. The objectives of this paper are to investigate the following two problems: 1) Identify among several classes of matrices with variants of the diagonal dominance property those which form pairs of incomparable classes. 2) If ( X1, X 2 ) is a pair of incomparable classes of matrices in n×n with variants of the diagonal dominance property, provide sufficient conditions for matrices in Xi to be in X j , where {i, j} = {1, 2}. The set of all matrices, which are diagonally similar to A ∈ n×n , is denoted by ( A).
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