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From Wikipedia, I learned that an affine transformation between two vector spaces is a linear mapping followed by a translation.

But in a book Multiple view geometry in computer vision by Hartley and Zisserman:

An affine transformation (or more simply an affinity) is a non-singular linear transformation followed by a translation.

I wonder if these are two different concepts, given that one does not require the linear transformation to be non-singular while the other does?

Thanks!

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    I think the definition of an affine transformation between two vector spaces is as follows. A map $f:V\to W$ is affine if there exists a $w$ in $W$ such that the map $v\mapsto f(v)-w$ is linear. In words, an affine transformation is a linear transformation up to a translation.2011-12-24

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