Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8953099 | Linear Algebra and its Applications | 2018 | 6 Pages |
Abstract
Recently Brent et al. presented new estimates for the determinant of a real perturbation I+E of the identity matrix. They give a lower and an upper bound depending on the maximum absolute value of the diagonal and the off-diagonal elements of E, and show that either bound is sharp. Their bounds will always include 1, and the difference of the bounds is at least tr(E). In this note we present a lower and an upper bound depending on the trace and Frobenius norm ϵ:=âEâF of the (real or complex) perturbation E, where the difference of the bounds is not larger than ϵ2+O(ϵ3) provided that ϵ<1. Moreover, we prove a bound on the relative error between detâ¡(I+E) and expâ¡(tr(E)) of order ϵ2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Siegfried M. Rump,