Continuous Dependence of Coefficients
The n roots of a polynomial of degree n depend continuously on the coefficients.
This result implies that the eigenvalues of a matrix depend continuously on the matrix. A proof can be found in a book of Tyrtyshnikov (see section References below).
The problem of approximating the roots given the coefficients is ill-conditioned. See, for example, Wilkinson's polynomial.
Read more about this topic: Properties Of Polynomial Roots
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