Show that orthogonal projection of $(0,1,0)$ over $W$ is the vector $(\frac{1}{\sqrt{2}}, \frac{i}{2}, \frac{1+i}{4})$

38 Views Asked by At

Given $W = Sp\{(1,i,0),(1,2,1-i)\}$ a subspace of $\mathbb{C}^3$ with the standard inner product.

Show that the orthogonal projection of $(0,1,0)$ over $W$ is the vector $(\frac{1}{\sqrt{2}}, \frac{i}{2}, \frac{1+i}{4})$.

I tried computing it but $W$ is not orthogonal, so how does one approach this problem?