503

Explain yourselves, comp sci. (mander.xyz)

submitted 4 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

71 comments fedilink hide all child comments

you are viewing a single comment's thread
view the rest of the comments

[-] muntedcrocodile@lemm.ee 2 points 4 months ago

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?

[-] chonglibloodsport@lemmy.world 10 points 4 months ago* (last edited 4 months ago)

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).

[-] i_love_FFT@lemmy.ml 1 points 4 months ago* (last edited 4 months ago)

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 d^2^x^6^, 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.

[-] Crazazy@feddit.nl 1 points 4 months ago

That's only if you're working with the perspective of it being a polynomial. When you're considering the polynomial as a vector however, that operation simply doesn't exist