It's a dynamically-sized list of objects of the same type stored contiguously in memory.
It's like a fancy list.
So is a wedding gift registry.
No, this is Patrick!
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.
Which is why you should:
Vec doubles in size every time it runs out of space)Memory is fairly cheap. Allocation time not so much.
matlab likes to pick the smallest available spot in memory to store a list, so for loops that increase the size of a matrix it's recommended to preallocate the space using a matrix full of zeros!
Many things like each other lined up in a row, and you can take some away or put more in.
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.
Did nobody else's CS department require a bunch of linear algebra courses? A vector is an element of vector space.
Sets are just objects in the category of Set.
That is quite possibly the least helpful answer you could give.
Also the most correct :)
Q: what is a vector? A: it is a vector
We do and we know this. Maybe programmers would give that answer
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.
It's not a terrible name, since it's derived from the mathematical construct of vectors as n-tuples. In the case of vectors in programming, n relates to the size of the underlying array, and the tuple consists of the elements of the vector.
I myself was confused, when I first saw what a vector did in practice.
Really bad name.
But then I didn't take Comp Sci.
The only correct answer for a 101 introduction. It’s an incredible powerful intuition even in contexts where vectors are seemingly used as a list of numbers.
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.
Singularities, too.
/dev/null
Tensors are easy!
It’s just a fancy list of fancy lists! :D
you just need to car and cdr your cons cell …
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.
I asked my math friend. He said a vector is magnitude plus velocity.
It should be magnitude plus orientation, not velocity. Velocity itself is a vector quantity
As a mathematician this genuinely hurts. Lol.
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.
Functions from the reals to the reals are an example of a vector space with elements which can not be represented as a list of numbers.
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