A (potential) projection operator Let $I$ be a 3-by-3 identity matrix and $\hat n$ be a unit vector orthonormal to some surface. What then does $I-\hat n\hat n$ mean geometrically? Also what does it mean to multiply this matrix/operator by a vector $v$? Some sort of projection?
Also, I don't understand what $\hat n\hat n$ means. Dimensionally it should be a 3-by-3 matrix because $I$ is such, right? 

If $n$ is a column vector (as usual in most linear algebra textbooks), then $\hat n\hat n$ would probably mean $\hat n \hat n^{T},$ which is the projection in the direction of $\hat n.$
And $(I - \hat n \hat n) v$ is the vector that resembles the projection vector from the tip of $v$ into the plane. You can see it if you expand $(I - \hat n \hat n) v$. You get $v - v_n$ where $v_n$ is the projection of $v$ onto the direction of $n.$
You can see in the following image: $v - v_n = e$

