@article{1d55eac321fa41a9b0403aeb1a6b6a27, title = "On the condition of the zeros of characteristic polynomials", abstract = "We prove that the expectation of the logarithm of the condition number of each of the zeros of the characteristic polynomial of a complex standard Gaussian matrix is Ω (n) (the real and imaginary parts of the entries of a Gaussian matrix are independent standard Gaussian random variables). This may provide a theoretical explanation for the common practice in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.", keywords = "Characteristic polynomial, Condition, Eigenvalues, Random matrices", author = "Peter B{\"u}rgisser and Felipe Cucker and {Rocha Cardozo}, Elisa", year = "2017", month = oct, doi = "10.1016/j.jco.2017.03.004", language = "English", volume = "42", pages = "72--84", journal = "Journal of Complexity", issn = "0885-064X", publisher = "Academic Press", }