Primitive symmetric matrices and their preservers

Beasley, LeRoy B.; Shi, Song

doi:10.1080/03081087.2016.1175414

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Introduction and Main Results1

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2018

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Cited by 3 publications

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“…Particularly, Minc [9] characterized those linear transformations that maps nonnegative matrices into nonnegative matrices and preserves the spectrum of each nonnegative matrix. In [1,2,3,4], linear maps preserving certain combinatorial properties of matrices are studied.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Linear maps on nonnegative symmetric matrices preserving the independence number

Hu¹,

Huang²

2018

Preprint

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The independence number of a square matrix A, denoted by α(A), is the maximum order of its principal zero submatrices. Let S + n be the set of n × n nonnegative symmetric matrices with zero trace, and let J n be the n × n matrix with all entries equal to one. Given any integers n, t with 2 ≤ t ≤ n − 1, we prove that a linear map φ :if and only if there is a permutation matrix P such that φ(X) = P T XP for all X ∈ S + n .

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