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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.
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.
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.
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.
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.
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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).
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).
I asked my math friend. He said a vector is magnitude plus velocity.
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.
It still can be, just not on infinite precision as nothing can with fp.
But the vector space of (all) real functions is a completely different beast from the space of computable functions on finite-precision numbers. If you restrict the equality of these functions to their extension,
defined as f = g iff forall x\in R: f(x)=g(x),
then that vector space appears to be not only finite dimensional, but in fact finite. Otherwise you probably get a countably infinite dimensional vector space indexed by lambda terms (or whatever formalism you prefer.) But nothing like the space which contains vectors like
F_{x_0}(x) := (1 if x = x_0; 0 otherwise)
where x_0 is uncomputable.
you just need to
carandcdryourconscell …As a mathematician this genuinely hurts. Lol.
This might hit harder if it weren’t for the fact that words very can have multiple senses
