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Matrices totally positive relative to a tree. (English) Zbl 1171.15021
Summary: It is known that for a totally positive (TP) matrix, the eigenvalues are positive and distinct and the eigenvector associated with the smallest eigenvalue is totally nonzero and has an alternating sign pattern. Here, a certain weakening of the TP hypothesis is shown to yield a similar conclusion.

MSC:
15B48 Positive matrices and their generalizations; cones of matrices
15A18 Eigenvalues, singular values, and eigenvectors
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