Quick maths question

[Inquisitor]

And no, this isn't homework

Can two vectors of different numbers of dimension be added together? For example, can the 2-vector (2, 2) be added to the 3-vector (2, 2, 2) to give another 3-vector, (4, 4, 2) , or is this not a valid thing to do?

None of the sites I've looked on seem to address this.

 

[Una]

Edit: oh yeah you can.

 

[spirit]

vector (2,2) is the same as (2,2,0) [if i remember right] so i don't see why not.

 

[Ricochet J]

As long as you get your place values correct, why not?

 

[Inquisitor]

As long as you get your place values correct, why not?

vector (2,2) is the same as (2,2,0) [if i remember right] so i don't see why not.

This is what I was thinking, but I wanted to be sure that it wasn't something that strictly speaking shouldn't or can't be done.

 

[spirit]

well i'm sure you can, i've done it loads of times when i was doing f.maths last year (but i don't think any alevels q's required it).

However, since i haven't done any maths of note for a year i wouldn't really trust myself (although i did teach the SAT & SAT subject tests lol - what a joke they are)

 

[Amleto]

technicaly speaking, I dont think it should be done. eg, I know you shouldn't add matrices of different sizes together.

Things like dot products/cross products don't work with differing dimensions. '+' signs should only be used in 'their' space, so adding different dimensions makes no sense. It's perfectly allowable to map a R^2 vector to an R^3 vector, and then add away, though

 

[Una]

Thats what I was thinking, you shouldnt really do it. But I guess if you have your reasons to do it, you can overload the + operator.

 

[Inquisitor]

Thanks guys

 

[carvegio]

why do you ask?
it is meaningless to add them and undefined

 

[Inquisitor]

It's part of a program I'm writing, and I was wondering whether or not I should allow it when adding two vectors.