I have noticed that when solving the following matrix-polynomial:

$$\sum_{k=0}^N{\bf C}_k{\bf T}^k = {\bf 0} \hspace{0.6cm} \text{ s.t. } \hspace{0.6cm} {\bf C}_k,{\bf T} \in\mathbb{R}^{{M\times M}}$$

using a numerical technique I can expand on if you wish, this solution is sometimes rather difficult to come by. But say that I can solve the equation system where multiply ${\bf C}_k$ with scalars $s_k$ and then manage to find a solution to this system:

$$\sum_{k=0}^{N}s_k{\bf C}_k{\bf T}^k={\bf 0} \hspace{0.6cm} \text{ s.t. } \hspace{0.6cm} {\bf C}_k,{\bf T} \in\mathbb{R}^{{M\times M}}, s_k \in \mathbb{R}$$

Is there any way I could the knowledge of such a solution in the pursuit of a solution to the first one..?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.