Matrix representation of a reflection

61 Views Asked by At

Assume I have a vector $v =$ $(-1, 1, -1)^T$ and $A$ is the relection through the plane orthogonal to $v$.
How would I find the matrix representation of A?

I have in my notes that the general formula of a reflection is
$A = $$I - 2(\frac{x.x^{T}}{x^{T}.x})$ and I know the inner product of orthogonal vectors is $0$, but I'm not sure how to do this question.