A silly doubt on Computer Science Objects: Arrays, Lists, Strings, and Vectors, are they the same concept? First of all I'm a Physics Student and I've been arguing with my brother concerning the usage and the fundamental meaning of a vector on Computer Science (CS).
I) Vectors
A vector have a axiomatic meaning, i.e., given a set $\mathcal{A}$ of objects, their objects can be called vectors if and only if they satisfy the vector space axioms $[1]$. Of course that, 3D vectors (little arrows), function, matrices and so on are different objects, but under a well defined vector addition $\boxplus$, and scalar multiplication $\boxdot$ they are the same: Vectors!
Furthermore, I think that is impossible to talk about more complicated objects like Tensors without a vector space structure underlying the mathematical usage of CS objects.
II) My doubt
So, I would like to know: arrays, lists, strings are the same object as vectors? In other words, they satisfy the vector space axioms?
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$[1]$ https://en.wikipedia.org/wiki/Vector_space#Definition
The objects you mention are not the same.
In particular, lists and (mutable) strings are dynamic data structures whereas arrays are not; their size is fixed.
Now, whether some set of instances of data structures forms a vector space depends on the underlying types, some do, others do not.
Considering e.g. boolean arrays of fixed size $n$ together with the usual addition/scalar multiplication of $\mathbb F_2^n$ yields a vector space, integer arrays of fixed size $n$ do not yield one with the usual operations.