It's a dynamically-sized list of objects of the same type stored contiguously in memory.
this post was submitted on 28 Apr 2024
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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:
- Preallocate the vector if you can guesstimate the size
- Use a vector library that won't reallocate the entire vector on every single addition (like Rust, whose
Vecdoubles 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!
Is that churn or chum? (RN or M)
Churm
Many things like each other lined up in a row, and you can take some away or put more in.
It's how you want an array to work.
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.
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So an ArrayList?
No. ArrayList is thread safe and implements the collections API. Vector doesn't. Though if you're using Java, there's almost no instance where you would want to use a Vector instead of ArrayList.
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
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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.
How are polynomials vectors how does that work?
Say u have polynomial f(x)= a + bx + cx^2 + dx^3
How is that represented as a vector? Or is it just one of those maths well technically things? Cos as far as I'm aware √g = π = e = 3.
Are differential eqs also vectors?
Your polynomial, f(x) = a + bx +cx^2 + dx^3, is an element of the vector space P3(R), the polynomial vector space of degree at most 3 over the reals. This space is isomorphic to R^4 and it has a standard basis: {1, x, x^2, x^3}. Then you can see that any such f(x) may be written as a linear combination of the basis vectors with real valued scalars.
As an exercise, you can check that P3(R) satisfies some of the properties of vector spaces yourself (existence of zero vector, associativity and commutativity of vector addition, distributivity of scalar multiplication over vector sums).
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Wouldn't N by M be a tensor? Magnitude and direction only need one entry per DOF.
Every vector is a tensor. Matrices are vectors because m by n matrices form vector spaces. Magnitude and direction have nothing to do with the definition of vectors which are just elements of vector spaces.
All vectors are tensors but not vice versa. And every page/definition of vector I've seen references magnitude and direction, even the vector space page you linked.
It looks like "vector" commonly refers to geometric vectors which is what most folks in this thread are discussing.
Would N by M vectors be imaginary, where each DOF has real and imaginary components?
Continuous functions on [0,1] are vectors. Magnitude and direction are meaningless in that vector space, usually called C[0,1]. Magnitude and direction are not fundamental properties of vectors.
n by m matrices (and the vector spaces to which they belong) are perhaps best thought of similarly to functions and function spaces. Not as geometric objects, but as linear transformations (which they are).
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.
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As a mathematician this genuinely hurts. Lol.
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
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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