Question

R^3 is a inner product space over the inner product

<(x1,x2,X3),(y1,y2,y3)> = x1y1+ x2y2 - x3y3

True or false with full explanation

Answer 1

for inner product:

$\langle u,u\rangle \ge 0$ with equality if and only if $u=0$

in our case:

$\langle x,x\rangle =x_1^2+ x_2^2 - x_3^2$ is not always > 0

so, this is not inner product

Answer: false