# Math Help - Linear Algebra Help - Question 1 !

1. ## Linear Algebra Help - Question 1 !

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

2. properties 1, 2 and 3 seem good, but 4 fails.

consider $u=(1,2)^T$ then $ = (1*1)-(2*2)=-3 \not \geq 0$