Before revision: To state the additional two matrix differential equations it is convenient to introduce the following two matrices: Then the two additional matrix differential equations that complete the OPE are as follows: almost everywhere, almost everywhere, with Here * denotes the group generalized inverse or Drazin inverse that is unique and given by where + denotes the Moore-Penrose pseudoinverse.
After revision: To state the additional two matrix differential equations it is convenient to introduce the following two matrices: Then the two additional matrix differential equations that complete the OPE are as follows: almost everywhere, almost everywhere, with Here * denotes the group generalized inverse or Drazin inverse that is unique and given by where + denotes the Moore–Penrose pseudoinverse.