MathLiveLinearity of a linear map
This defining condition says a map T respects vector addition and scalar multiplication, so the image of a combination equals the same combination of images. It is used to check whether a function between vector spaces is linear.
T(\alpha \mathbf{x} + \beta \mathbf{y}) = \alpha T(\mathbf{x}) + \beta T(\mathbf{y})What the symbols mean
| the linear map (a function from one vector space to another) | |
| scalars (real numbers in the stated setting) | |
| vectors in the domain of T |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledlinear map definition, linear transformation property, superposition principle, linearity condition, linear mapping property, additivity and homogeneity
- SourceWikidata Q207643
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