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Matrices totally positive relative to a tree, II

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URI: https://hdl.handle.net/10016/23404
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matrices_LAA_2016_ps.pdf (510.55 KB)
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2016-09-15
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Elsevier
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Abstract
If T is a labelled tree, a matrix A is totally positive relative to T , principal submatrices of A associated with deletion of pendent vertices of T are P-matrices, and A has positive determinant, then the smallest absolute eigenvalue of A is positive with multiplicity 1 and its eigenvector is signed according to T . This conclusion has been incorrectly conjectured under weaker hypotheses.
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Graph, Neumaier conclusion, Spectral theory, Sylvester’s identity, Totally positive matrix, Totally positive relative to a tree
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Linear Algebra and its Applications, 2016, v. 505, pp. 1-10.
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