Comment on Explain yourselves, comp sci.

<- View Parent
GnomeKat@lemmy.blahaj.zone ⁨7⁩ ⁨months⁩ ago

Its the algebraic properties that are important, not all vectors are n-tuples, eg the set of polynomials of degree less than n.

You need a basis to coordinate a vector, you can work with vectors without doing that and just deal with the algebraic properties. The coordinate representation is dependent on the basis chosen and isn’t fundamental to the vector. So calling them n-tuples isn’t technically correct.

You can turn them into a set of coordinates if you have a basis, but the fact that you can do that is because of the algebraic properties so it’s those properties which define what a vector is.

source
Sort:hotnewtop