Can we get the derivative of a Toeplitz function?

Question

Like 'Toeplitz(c,r)', which means a Toeplitz matrix formed by a column vector 'c' and a row vector 'r'. Can we get the derivatives of this function?

Like $\frac{\partial{\text{Toeplitz}(c,r)}}{\partial c}$?

Answer 1

Well, if your Toeplitz matrix is given by the function $$\eqalign{ T &= {\rm Toeplitz}(c,r) \cr }$$ then its gradient with respect to the $k^{th}$ component of the $c$ vector is the matrix $$\eqalign{ \frac{\partial T}{\partial c_k} &= {\rm Toeplitz}(e_k,0) \cr }$$ where $e_k$ is the $k^{th}$ vector of the standard cartesian basis.