element on the surface moves with the surface. Therefore, we see that transforms one unit vector on the boundary to another unit vector on the boundary, in other words, it is orthogonal, i.e., . In a similar manner as before, we can define another anti-symmetric matrix as

where its dual is defined as (and ). The Dirichlet's ellipsoidal problem then reduces to finding whether the matrix exists that determines the vector and that it is expressible in terms of two orthogonal matrices as