Fast locality-sensitive hashing
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
On Explicit Recursive Formulas in the Spectral Perturbation Analysis of a Jordan Block
SIAM Journal on Matrix Analysis and Applications
Computing Characteristic Polynomials from Eigenvalues
SIAM Journal on Matrix Analysis and Applications
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We derive absolute perturbation bounds for the coefficients of the characteristic polynomial of a $n\times n$ complex matrix. The bounds consist of elementary symmetric functions of singular values, and suggest that coefficients of normal matrices are better conditioned with regard to absolute perturbations than those of general matrices. When the matrix is Hermitian positive-definite, the bounds can be expressed in terms of the coefficients themselves. We also improve absolute and relative perturbation bounds for determinants. The basis for all bounds is an expansion of the determinant of a perturbed diagonal matrix.