linguistic:voice_change, linguistic:paraphrasing
In more than two dimensions

While n̂ is not well-defined in more than two dimensions, this can be generalized to any number of dimensions by noting that n̂ n̂ is simply the symmetric matrix with all eigenvalues unity except for a zero eigenvalue in the direction along the line providing a seminorm on the distance between p and another point giving the distance to the line. In any number of dimensions, if v̂ is a unit vector along the i th line, then

where I is the identity matrix, and so