where its dual is defined as Λ Λ i j ∗ ∗ = ε ε i j k Λ Λ k (and 2 Λ Λ i = ε ε i j k Λ Λ j k ∗ ∗ ). The Dirichlet's ellipsoidal problem then reduces to finding whether the matrix P ( t ) exists that determines the vector X ( t ) and that it is expressible in terms of two orthogonal matrices as in P = L T A S where, further