If $$y(x) = \xi_1+\xi_2+\xi_3$$ whenever $x = (\xi_1,\xi_2,\xi_3)$ is a vector in C^3, then y is a linear functional on C^3; find a basis of the subspace consisting of all those vectors x, for which[x,y]=0
Please, help

Question

If $$y(x) = \xi_1+\xi_2+\xi_3$$ whenever $x = (\xi_1,\xi_2,\xi_3)$ is a vector in C^3, then y is a linear functional on C^3; find a basis of the subspace consisting of all those vectors x, for which[x,y]=0
Please, help

loser66 · Answer

@ikram002p

ikram002p · Answer

$$y=\epsilon_1+\epsilon_2+\epsilon_3$$
$$ [x,y]=0$$
i only need u to define wat is [x,y]  ok ?
if subspace H from C
s.t
$$H={1,-1,i,-i}$$

loser66 · Answer

It is easy to see [x,y]=0 by H = 1,-1,i,-i
but how to get it?

ikram002p · Answer

i just need the difenition of [....]
ithats wat i ment
ok ill check the txt book and see wat i cud find