modular mappings in vector spaces over the field of complex numbers


Suppose X is a -vector space. A mapping ρ:X[0,] is called modular if the following three conditions are satisfied:

  1. 1.

    ρ(x)=0 if and only if x=0.

  2. 2.

    ρ(αx)=ρ(x) for all xX and for all scalars α such that |α|=1.

  3. 3.

    ρ(αx+βy)ρ(x)+ρ(y) for all x,yX and for all scalars α and β such that α+β=1 and α,β0.

Title modular mappings in vector spaces over the field of complex numbersMathworldPlanetmathPlanetmath
Canonical name ModularMappingsInVectorSpacesOverTheFieldOfComplexNumbers
Date of creation 2013-03-22 16:08:12
Last modified on 2013-03-22 16:08:12
Owner gilbert_51126 (14238)
Last modified by gilbert_51126 (14238)
Numerical id 11
Author gilbert_51126 (14238)
Entry type Definition
Classification msc 46-00
Defines modular