TITLE: Question about definition: what is an affine linear space?
QUESTION [7 upvotes]: In an article I am reading it says : Let $H$ be an affine linear space of codimension $m$...
Could someone please explain me what is meant by affine linear space?
Thanks!

REPLY [4 votes]: "Let H be an affine linear space of codimension $m$"
what is meant by affine linear space?

There are two related meanings: $H$ is not required to contain $0$, and $H$ is not required to have any of its points distinguished as an "origin".  For the phrase in the question to make sense, $H$ should be inside a linear space that has a distinguished origin.
In practice it means $H$ is cut out by linear equations that are allowed to have nonzero constant terms, or is the image of a non-homogeneous vector-valued linear function $Ax + b$.  The minimum number of inhomogeneous linear equations necessary to define $H$ is the codimension $m$.