Properties of sub-matrices of Sylvester matrices and triangular toeplitz   matrices
  In this note we discover and prove some interesting and important relations among sub-matrices of Sylvester matrices and triangular toeplitz matrices. The main result is Hill's identity discovered by R. D. Hill which has an important application in optimal control problems. 
Yousong Luo, Robin Hill and Uwe Schwerdtfeger
math.OC