An affine function on a real or complex vector space has the form , where is a linear map and is constant. Its derivative is the constant map . It is linear exactly when .
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The term is not very clear, as it could either mean:
- a real number function whose graph is a line, i.e.:or for higher dimensions, a hyperplane:
- a linear map. Note that the above linear functions are not linear maps unless (known as the homogeneous case), because e.g.:butFor this reason, it is better never to refer to linear maps as linear functions.