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:

$\langle x,x\rangle \ge 0$

in our case:

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

so, R^3 is a not inner product space over the inner product

statement is false