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 Lozinskiń≠ 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.

Read more about Logarithmic NormOriginal Definition, Alternative Definitions, Properties, Example Logarithmic Norms, Applications in Matrix Theory and Spectral Theory, Applications in Stability Theory and Numerical Analysis, Applications To Elliptic Differential Operators, Extensions To Nonlinear Maps

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 ...

Famous quotes containing the word norm:

    As long as male behavior is taken to be the norm, there can be no serious questioning of male traits and behavior. A norm is by definition a standard for judging; it is not itself subject to judgment.
    Myriam Miedzian, U.S. author. Boys Will Be Boys, ch. 1 (1991)