Before revision:  Here H\!K{\cal  _A(t) is a 1-parameter varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.
After revision:  Here H\!K{\cal F _A(t) is a 1-parameter varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.