TY - JOUR
T1 - Matrices totally positive relative to a tree, II
AU - Costas-Santos, R.S.
AU - Johnson, C.R.
JO - Linear Algebra and its Applications
VL - 505
SP - 1
EP - 10
PY - 2016
DA - 2016/09/15/
SN - 0024-3795
DO - https://doi.org/10.1016/j.laa.2016.04.021
UR - https://www.sciencedirect.com/science/article/pii/S0024379516301203
KW - Graph
KW - Neumaier conclusion
KW - Spectral theory
KW - Sylvester's identity
KW - Totally positive matrix
KW - Totally positive relative to a tree
AB - 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.
ER -