A class of oscillatory matrices with exponent \(n - 1\)
The authors describe the class of \(n\times n\) oscillatory matrices which have maximal exponent equal to \(n-1\). \textit{F. P. Gantmacher} and \textit{M. G. Krein} [Oscillation matrices and kernels and small vibrations of mechanical systems. (2002; Zbl 1002.74002)] laid the groundwork for the theory of oscillatory matrices. They proved that the eigenvalues of an oscillatory matrix are real, positive, and distinct. In the paper of \textit{S. M. Fallat, M. Fiedler} and \textit{T. L. Markham} [Linear Algebra Appl. 359, No.~1--3, 79--90 (2003; Zbl 1026.15008)] a question was raised about describing the \(n\times n\) oscillatory matrices whose exponent is equal to \(n-1\). This class is completely characterized in this paper.
totally positive and nonnegative matrices
scientific article; zbMATH DE number 5167490