We chose the positive square root because we usually de?ne sin?1 x to have outputs between ?π/2 and π/2, and the cosine function is always positive on this interval. When dealing with inverse functions we are often faced with choices like this; when in doubt draw a graph and be ...
In fact, from |ni(x)|2=1 we deduce by differentiation that niT(x)Si(x)=0. This, together with the fact that ni⊗ni is the projection onto the normal of the hypersurface Si shows that Pi(x)Dni(x)=Dni(x). With our choice of signs for di, the symmetric matrices Si are ...
where[Math Processing Error]is the unit square or the unit cube and[Math Processing Error],[Math Processing Error]denotes the invertible transformation of the reference element