# Logarithmic Norm

In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist and Sergei Lozinskiĭ in 1958, for square matrices. It has since been extended to nonlinear operators and unbounded operators as well. The logarithmic norm has a wide range of applications, in particular in matrix theory, differential equations and numerical analysis.

### Other articles related to "logarithmic norm, norm, logarithmic":

Logarithmic Norm - Extensions To Nonlinear Maps
... For nonlinear operators the operator norm and logarithmic norm are defined in terms of the inequalities where is the least upper bound Lipschitz constant of, and is the greatest lower bound ... Here is the least upper bound logarithmic Lipschitz constant of, and is the greatest lower bound logarithmic Lipschitz constant ... then and Here is the Jacobian matrix of, linking the nonlinear extension to the matrix norm and logarithmic norm ...

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