Sorry for many questions in this part. But I am still confused about the following:
From textbook "Optimization by vector space"(Luenberger):
Problem:
I read the def. of quotient space many times; however, I find the def. of quotient space is very like to the description above ($x +$ subspace). It seems affine subspace is one of quotient space. Is it true?
What on earth is the difference between them?
Yes, each element of a quotient of a vector space by a subspace is precisely a translation of that subspace, that is, a linear variety.