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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.
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.
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.
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.
ArrayList isn’t thread-safe, though…
Thread safe as in it raises an exception instead of breaking your list.
Only if one thread modifies it while another one is iterating over it, if two threads try to modify the list at once there isn’t any kind of synchronization and it really could break your list.
For everything else, there’s
Collections.synchronizedList(new ArrayList<>())
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.
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.
Yes, and as linear algebra teaches, to convert a vector from direction and magnitude to a list of numbers (components), follow these steps:
- Let the magnitude of the vector be represented by the symbol |A| or A.
- Let the direction of the vector be represented by the angle θ, which is measured counterclockwise from the positive x-axis.
- The x-component of the vector is given by: Ax = |A| cos(θ)
- The y-component of the vector is given by: Ay = |A| sin(θ)
The vector can now be represented as a list of numbers: A = (Ax, Ay)
For example, if a vector has a magnitude of 5 units and a direction of 30° counterclockwise from the positive x-axis, its components would be:
Ax = 5 cos(30°) ≈ 4.33 units Ay = 5 sin(30°) ≈ 2.50 units
The vector can now be written as A = (4.33, 2.50)
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.
Tensors are easy!
It’s just a fancy list of fancy lists! :D
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®, 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® 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).
What happens to elements with powers of x above 3? Say we multiply the example vector above with itself. We would end up with a component d2x6, witch is not part of the P3R vector space, right?
Do we need a special multiplication rule to handle powers of x above 3? I’ve worked with quaternions before, which has " special" multiplication rules by defining i j and k.
Multiplication of two vectors is not an operation defined on vector spaces. If you want that, you’re looking at either a structure known as an inner product space or an algebra over a field.
Note that the usual notion of polynomial multiplication doesn’t apply to polynomial vector spaces, nor does it agree with the definition of an inner product nor the bilinear product of an algebra.
As a mathematician this genuinely hurts. Lol.
I asked my math friend. He said a vector is magnitude plus velocity.
This might hit harder if it weren’t for the fact that words very can have multiple senses
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.
