We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σ i (A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ 1 and σ 2. The pairs σ, σ 1 and σ 1, σ 2 must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ 1 in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ 1 and σ 2 in common.
Positivity – Springer Journals
Published: Jul 11, 2006
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