The discussion revolves around defining the zero vector in a modified vector space with non-standard operations for vector addition and scalar multiplication. Participants are exploring the implications of these operations on the identification of the zero vector and the additive inverse.
Some participants have provided guidance on how to approach finding the zero vector by suggesting to solve the equation derived from the modified addition operation. There is ongoing exploration of the additive identity and its properties, with participants questioning their own reasoning and seeking confirmation of their findings.
Participants express confusion about the non-standard operations and their implications for traditional vector space concepts. There is a recognition that the zero vector in this context may not be (0,0) as typically expected, leading to further investigation of the definitions involved.
LCKurtz said:Yes in ##R^2## but not in your problem. That isn't your rule for scalar multiplication.
LCKurtz said:Yes that is correct. I don't think we need to beat this horse any more. But using these techniques you could verify all the axioms of a vector space work even though its arithmetic rules may seem bizarre. To paraphrase, "This ain't your daddy's vector space".
LCKurtz said:The additive inverse of (x,y) is the vector (a,b) you can ⊕ to (x,y) and get the additive identity.
s_nirmit said:how do you find the -v vector then ?
s_nirmit said:is it -v= (1-x), (-2-y) ?