Root spreads for polynomials and Hermitian matrix pencils
Let \(f(x)\) be a polynomial with real roots \(x_ 1,\dots,x_ n\) and let be \(f_ i(x)\), \(i= 1,\dots, n\) be certain linear combinations of the polynomials \(f(x)/(x- x_ i)\). The spread of a polynomial is the difference of its largest and smallest root. The author compare the spreads of \(f(x)\) and of the \(f_ i(x)\). This is applied to the spreads of the eigenvalues of an Hermitian matrix and the spreads of its principal submatrices.
scientific article; zbMATH DE number 769037