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
Comment on Explain yourselves, comp sci.
i_love_FFT@lemmy.ml [bot] 2 months agoWhat 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^2x^6, witch is not part of the P3R vector source, 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 2 months ago
chonglibloodsport@lemmy.world 2 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. For that you need an algebra.