# Notation question: dual space basis

I have an exercise that I am trying to decipher, but as I have never seen this notation before I do not know how to read it. The problem states:

The vectors $$x_1=(1,1,1),x_2=(1,1,-1)$$ and $$x_3=(1,-1,-1)$$ form a basis of $$\mathbb{C}^3$$. If $${y_1,y_2,y_3}$$ is the dual basis, and if $$x=(0,1,0)$$, find $$[x,y_1],[x,y_2],[x,y_3]$$.

Can someone help me understand what this last part $$[x,y_i]$$ means?

• Welcome to Mathematics Stack Exchange. It could be the inner product – J. W. Tanner May 31 at 18:56

If $$V$$ is a vector space, $$y \in V'$$ (the dual space of $$V)$$ and $$x \in V$$, the notation $$[x, y]$$ stands for the scalar $$y(x)$$, which one obtains when one inserts $$x$$ into $$y$$. It is explained in the text why this notation is used.
• Right, that notation, $y(x)$, is what I am used to. That solves it. – Jake May 31 at 19:06