Matrix of feature Vectors and Eigen values

I want to create a feature vector X(i) = {m_1i m_2i m_3i ......m_ki} and I want to do matrix operations taking X(i)'s as elements of matrices. Say I want to define an NxN distance matrix between X(i) and X(j) such that D(Xi,Xj) = X(i)-X(j) and I want to get eigen values for the matrix containing vectors

Can you please explain which data structures to use instead of using 3D matrices?