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It’s a dynamically-sized list of objects of the same type stored contiguously in memory.
It’s like a fancy list.
It’s a dynamically-sized list of objects of the same type stored contiguously in memory.
dynamically-sized: The size of it can change as needed.
list: It stores multiple things together.
object: A bit of programmer defined data.
of the same type: all the objects in the list are defined the same way
stored contigiously in memory: if you think of memory as a bookshelf then all the objects on the list would be stored right next to each other on the bookshelf rather than spread across the bookshelf.
Dynamically sized but stored contiguously makes the systems performance engineer in me weep. If the lists get big, the kernel is going to do so much churn.
Contiguous storage is very fast in terms of iteration though often offsetting the cost of allocation
Modern CPUs are also extremely efficient at dealing with contiguous data structures. Branch prediction and caching get to shine on them.
Avoiding memory access or helping CPU access it all upfront switches physical domain of computation.
No, it’s an n-tuple with certain algebraic properties.
This is such an understated but useful description in this context. It’s also how I understood algebra for applied matrix computation.
I was just coming down from THC when I wrote this, so I’m extra jazzed you liked it. 😁
Edit: also, love the username.
Its the algebraic properties that are important, not all vectors are n-tuples, eg the set of polynomials of degree less than n.
You need a basis to coordinate a vector, you can work with vectors without doing that and just deal with the algebraic properties. The coordinate representation is dependent on the basis chosen and isn’t fundamental to the vector. So calling them n-tuples isn’t technically correct.
You can turn them into a set of coordinates if you have a basis, but the fact that you can do that is because of the algebraic properties so it’s those properties which define what a vector is.
I think a better example to show how vectors don’t necessarily need to be what people conceptualize as n-tuples would have been the real numbers. (Of course, these can be considered 1-tuples, but the same can be said of any arbitrary set element that is not itself a tuple with more entries.) A cooler example would have been R[x] (the ring of real-valued polynomials of a single variable) especially since an isomorphic ring using n-tuples would be a more cumbersome representation of the algebra.
Ooh, do tensors next!
You should ask your biologist friend and your physicist friend and your compsci friend to debate about what vectors are. Singularities, too.
you just need to
carandcdryourconscell …What do you mean? A vector is a direction and magnitude!
Maybe they mean std::vector in C++?
It’s a terrible name. The math answer is what I would give.
Did nobody else’s CS department require a bunch of linear algebra courses? A vector is an element of vector space.
Well mathematically isn’t it an n by 1 matrix.
Not always. Any m by n matrix is also a vector. Polynomials are vectors. As are continuous functions.
A vector is an element of a vector space over a field. These are sets which have a few operations, vector addition and scalar multiplication, and obey some well known rules, such as the existence of a zero vector (identity for vector addition), associativity and commutativity of vector addition, distributivity of scalar multiplication over vector sums, that sort of thing!
These basic properties give rise to more elaborate concepts such as linear independence, spanning sets, and the idea of a basis, though not all vector spaces have a finite basis.
It’s an array.
First time I heard of vectors in comp-sci was in C++. The naming still doesn’t make sense to me.
A vector is a list of numbers, at its most basic. You can add a lot of extra functionality to it, but at its core, its just a list.
