Solving this matrix equation

51 Views Asked by At

Suppose $\mathbf{c}(\theta)$ is a known parametric circular curve in $\mathbb{R}^3$.

How could we go about solving the following for $\theta$?

$$(\mathbf{x}-A\mathbf{c}(\theta))^TBA\mathbf{c}'(\theta)=0$$

where

  • $B=(I-\frac{1_{4\times4}D}{Tr(D)})^TD$
  • $D\in\mathbb{R}^{4\times4}$ is a diagonal matrix
  • $1_{4\times4}$ is a matrix with all elements equal to 1.
  • $A=\begin{bmatrix}-1&-1&-1\\1&-1&-1\\1&1&-1\\1&1&1\end{bmatrix}$