Hello, I have a question about what I would call, for want of a better name, matrix decomposition. However, my question does not concern standard decompositions like eigenvalue or Cholesky decomposition. The problem: Assume given two real and square matrices C and D. C is symmetric, while D is antisymmetric. Find two real and square matrices A and B, such that: C = A*A - B*B and D = A*B + B*A Here * denotes standard matrix multiplication. Does anybody know a suitable algorithm for this or a similar problem? Most likely several solutions A and B exist. This problem arises when trying to describe radar Doppler measurements of hydrometeors (cloud and rain drops). Any help will be appreciated.