I'm trying to understand the historical context behind the word pencil in matrix pencils, or pencil of curves so on.
I am aware that even Gantmacher 1959 has this terminology however I don't know where it originates from. I am also curious what he uses in the original Russian version in place for that word (though I don't know any Russian, I can handle a literal translation ala Körper etc.).
EDIT Since there are answers given towards the meaning of the word "pencil" which is really good to know, I would appreciate if the context is also taken into account. It is from the definition of the pencil forms that some sort of bundling or parameterization is involved. However the definition itself of the word pencil does not introduce the context.
Compare it with the word affine which comes from the similar meaning (Latin affinis) "adjacent,connected" but this is not preferred for some reason although the structure of matrix pencils resembles $a\lambda – b$ more an affine transformation in my opinion. Obviously, it might be a nonlinear function of $\lambda$ but that context looks like long forgotten (until recently the computational tools for quadratic and nonlinear eigenvalue problems started to emerge).
Thus, I would speculate that some circles deliberately avoided either pencil or the affine word at some point. That's what I would like to understand.
Best Answer
The Oxford English Dictionary has an example from 1665 of "pencil" in the sense of "A group of rays or a beam of radiation converging to or diverging from a point." And one from 1840 in the geometric sense of "A set of lines meeting in a point"