Zeros of Arbitrary Polynomials as Eigenvalues of Simple Matrices

摘要

An NxN matrix, whose N eigenvalues coincide with the N zeros of the generic polynomial PN(x) of precise degree N, is explicitly defined in terms of N arbitrary numbers yj and of the N values Fi=F(yj) that the logarithmic derivative of PN(x),F(x)=P'N(x)/Pn(x) takes at the N points yj.