Prove that the set of conditions:
L(u+v) = L(u)+L(v)
L(cv) = cL(v)
(valid for all vectors u, v, and any scalar c)
Is equivalent to the single condition:
(For all vectors u, v and any scalars r, s)
I understand obviously that additivity and homogeneity conditions are being combined into one condition.
I understand that I have to do a biconditional proof going from 1=>2 and then proving 2=>1 but I'm having trouble with the mechanics.
Just for fun : what is this new condition called? I heard superposition and/or convulsion. Please enlighten me