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单词 ZeroMap
释义

zero map


DefinitionSuppose X is a set, and Y is a vector spaceMathworldPlanetmath with zero vector 0.If Z is a map Z:XY, such that Z(x)=0 for all x in X,then Z is a zero map.

0.0.1 Examples

  1. 1.

    On the set of non-invertible n×n matrices, the determinantMathworldPlanetmathis a zero map.

  2. 2.

    If X is the zero vector space, any linear map T:XY isa zero map. In fact, T(0)=T(00)=0T(0)=0.

  3. 3.

    If X=Y and its field is or , then the spectrum of Z is{0}.

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