A note on minimal norms and the logarithmic derivative of a matrix

Abstract

Let A denote an n × nmatrix with eigenvalues denote the maximum real part of {λ_i }. Relative to a subordinate matrix norm denote the logarithmic derivative of A. It is well known that . In this paper, necessary and sufficient conditions are given for the equality for a fixed matrix Aand for the set of matrices which are complex scalar multiples of A. The conditions are formulated in terms of minimal norms and in terms of the eigenvalues of A.

^†This research was supported in part by N.R.C. Grants A8214, A5233.

^†This research was supported in part by N.R.C. Grants A8214, A5233.

Notes

^†This research was supported in part by N.R.C. Grants A8214, A5233.