Consider a dataset $\ D $ of $n \times m$ which has a covariance matrix of $\ C(D) $.
Now say, $\ D $ is vertically divided into $\ k $ sets. Say, the covariance matrices of them are $\ C1, C2,....,Ck $.
How to merge $\ C1, C2,....,Ck $ to form $\ Cm $ in such a way that $\ Cm = C(D) $.