Logarithmic norm

In mathematics, the logarithmic norm is a real-valued functional on operators, constructed from either a vector norm or an inner product, or directly from the induced operator norm. It quantifies key notions such as positive/negative definiteness in matrix theory, uniformly coercive or monotone vector fields in nonlinear analysis, and strong ellipticity in differential operators on function spaces, subject to specific boundary conditions.

The logarithmic norm has a wide range of applications in matrix theory, stability theory for initial and boundary value problems in differential equations, in nonlinear analysis, applied mathematics, and numerical analysis.

Comprehensive treatments of the theory and its applications can be found in recent monographs, on which this article is based.