>>11900786>Well I had my shameful geometric vector questions.The most shameful question is that one never asks but is tormented by for the rest of their life.
>They can be considered as points if their beginning is the origin (in some spaces only apparently), fine, and they are also (directed) line segments because (I guess) they have a beginning and an end point and as such you can put a line through them.Yeah, you get the line segments with arrow tip pointing to some direction from the points and then realising that you can move either of its end points freely (as long as you do that to the other one also). This follows from the fact that the change in each coordinate is the same whether you start from the origin or some other point.
>Is what I said thus far correct?Seems good.
>So, does a geometric vector also codify a set of points (as a line segment)?Both (I mean they are equivalent so yeah) codify a set of points, namely a line. You can take any vector and define to get a line going to the direction of the given vector through the origin. If you know the length of your vector, you can use that and this set to obtain an explicit set of a points on a line segment starting at the origin and ending as far from it as you want. To move it around, you just do the translation like you had the lines y = kx + c back in school to move it around in your Euclidean space. A thing worth noting though: a translation is not a linear map unless it is the identity!
>Which then somehow are equivalent to other geo vectors with the same lenght and direction?Yes. The point is that your geometric vector anywhere is determined by the change in each coordinate, and this change is independent of the points themselves.
I hope I managed to ask your questions somewhat sufficiently. I am assuming we are talking about the Euclidean spaces. I hope the English isn't too broken.
