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BY 4.0 license Open Access Published by De Gruyter Open Access December 17, 2019

The almost semimonotone matrices

Megan Wendler EMAIL logo
From the journal Special Matrices


A (strictly) semimonotone matrix A ∈ ℝn×n is such that for every nonzero vector x ∈ ℝn with nonnegative entries, there is an index k such that xk > 0 and (Ax)k is nonnegative (positive). A matrix which is (strictly) semimonotone has the property that every principal submatrix is also (strictly) semimonotone. Thus, it becomes natural to examine the almost (strictly) semimonotone matrices which are those matrices which are not (strictly) semimonotone but whose proper principal submatrices are (strictly) semimonotone. We characterize the 2 × 2 and 3 × 3 almost (strictly) semimonotone matrices and describe many of their properties. Then we explore general almost (strictly) semimonotone matrices, including the problem of detection and construction. Finally, we relate (strict) central matrices to semimonotone matrices.

MSC 2010: 15A48; 90C33


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Received: 2019-09-18
Accepted: 2019-12-03
Published Online: 2019-12-17

© 2019 Megan Wendler, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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