A list is a vector? So I'm watching this video to learn about neural networks : https://www.youtube.com/watch?v=tMrbN67U9d4
At 9:07, the author says that in mathematics a list is a vector.
So for example, [0, 1, 7, 3, 2, 6] would be a vector.
I don't understand how. I thought that a vector was a set of derivatives coordinates, like dx:2 and dy:3 would be a 2d vector.
Would someone please explain in simple terms why a list can be considered a vector, and how it works ?
Thanks.
 A: That's programmer jargon. When a programmer talks about a vector it's often the same as an array or a tuple where all elements are of the same type.
For example, C++ comes with a vector class with description: "Vectors are sequence containers representing arrays that can change in size."
A: No need to think about derivatives, coordinates, or any of this extra stuff.
A vector is indeed just an ordered list of variables. That's all there is to it. $[1,2,3,4,5]$ is a perfectly good vector. As is $[x_1, x_2]$.
From there you can build all kinds of abstractions. For example, when you're looking at a cartesian grid, it's common to express $x$ and $y$ coordinates in a vector of form $[x,y]$.
If you want to be very formal and correct, a vector needs to belong to a vector space -- a set of vectors -- that satisfies some abstract requirements about adding vectors together, and about being able to multiply vectors by scalars. But that level of formality is not what you need at this level.
A: Consider $\mathbf{R}^n$. For example for $n=2$, you have $\mathbf{R}^2$. If $n>3$ then it can be complicated to visualize the space, but you can construct it.
Now, build what we call the canonical base $\{e_1,\dots,e_n\}$  where $e_1\dots e_n$ are vector of the form: $(1,0,\dots,0) \;\; \dots\;\; (0,0,\dots,1)$. Here, a general $n-$tuple of numbers represents a unique vector $v=(v_1,\dots,v_n)$.
