Note that because M αβ is defined as the tensor (dyadic) product of v α with itself, its eigenvalues are the norm of v α (with corresponding eigenvector v) and zero otherwise (with arbitrary eigenvectors orthogonal to v α ). The space of solutions to this equation can be constructed from the structure of the kernel of M αβ and its complement, the image of M αβ . Decomposing a solution Pα into the sum of two orthogonal parts I α ∈ Im(M) and N α ∈ ker(M), the condition transforms into the following set of decoupled equations: