Reflection around a plane, parallel to a line I'm supposed to determine the matrix of the reflection of a vector $v \in \mathbb{R}^{3}$ around the plane $z = 0$, parallel to the line $x = y = z$. I think this means that, denoting the plane by $E$ and the line by $F$, we will have $\mathbb{R}^{3} = E \oplus F$ and thus for a vector $v$, we write $v = z + w$ where $z \in E$ and $w \in F$, and then we set $Rv = z + Rw$? Then I guess we'd have $Rw = -w$ making $Rv = z - w$. Here $R$ denotes the reflection. Is this the correct definition?

The definition is exactly as stated in the question.
