properties 1, 2 and 3 seem good, but 4 fails.
consider then
Please help me in these problems
Determine which of the four inner product axioms do not hold. give a specific example in the case.
u v
[u1] [v1]
[u2] [v2]
Let u and v be in R^2.
define <u, v> = u1v1 - u2v2
axioms:
1) <u, v> = <v,u>
2) <u, v+w> = <u, v> + <u, w>
3) <cu, v> = c<u, v>
4) <u, u> greater than or equal to 0 if and only if u = 0