Estimates of the determinant of a perturbed identity matrix
The author presents bounds for the determinant of a real perturbation \(I + E\) of the identity matrix \(I\), depending on the trace \(\operatorname{tr}(E)\) of \(E\) and the Frobenius norm \(\varepsilon\) of the (real or complex) perturbation \(E\). It is assumed that the difference of the bounds is not larger than \(\varepsilon^2 + O(\varepsilon^3)\) provided that \(\varepsilon< 1\). Moreover, he proves a bound of order \(\varepsilon^2\) on the relative error between the above mentioned determinant and \(\exp({\operatorname{tr}}(E))\).
scientific article; zbMATH DE number 6951560