this post was submitted on 28 Apr 2024
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Science Memes

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Explain yourselves, comp sci. (mander.xyz)
submitted 6 months ago by [email protected] to c/[email protected]
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[–] [email protected] 1 points 6 months ago* (last edited 6 months ago) (2 children)

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.

[–] [email protected] 3 points 6 months ago* (last edited 6 months ago)

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.

[–] [email protected] 1 points 6 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