I have an orthogonal basis consisting of the following vectors in C^4 -
[0,1,0,-1] , [1,0,0,0] , [0,0,i,0]
Now, I have the vector [1, -i, 0, i] in standard coordinates. I wish to express this vector with respect to my orthogonal basis.
So, I solve c1 [0,1,0,-1] + c2 [1,0,0,0] + c3 [0,0,0,0] + c4[0,0,i,0] = [1, -i, 0, i].
[c1,c2,c3,c4] will be the vector wrt my othogonal basis.
Is this correct?