Quadratic realizability of palindromic matrix polynomials: the real case

Abstract

Let be a list consisting of structural data for a matrix polynomial; here is a sublist consisting of powers of irreducible (monic) scalar polynomials over the field , and is a sublist of nonnegative integers. For an arbitrary such , we give easy-to-check necessary and sufficient conditions for to be the list of elementary divisors and minimal indices of some real T-palindromic quadratic matrix polynomial. For a list satisfying these conditions, we show how to explicitly build a real T-palindromic quadratic matrix polynomial having as its structural data; that is, we provide a T-palindromic quadratic realization of over . A significant feature of our construction differentiates it from related work in the literature; the realizations constructed here are direct sums of blocks with low bandwidth, that transparently display the spectral and singular structural data in the original list .