Pentadiagonal oscillatory matrices with two spectrum in common (Q865011)

Let \(\sigma,\sigma_1,\sigma_2\) be the spectrum of a given symmetric pentadiagonal oscillatory (SPO) matrix \(A\) and of the matrices obtained by deleting from \(A\) the first or the first two rows and columns, respectively. The author discusses operations in terms of elementary matrices (a) for constructing from \(A\) a family of SPO matrices with common \(\sigma\) and \(\sigma_1\), and (b) for constructing from a totally positive matrix a family with common \(\sigma,\sigma_1, \sigma_2\).