How to find $B$ by solving the following linear system:
$s_k$ $B$ ${s_k}^T$ $=1,$ $\qquad$ for $k=1 ... ,p$.
Where $s_k$ is a $1\times3$ row_vector from the matrix
$S= [s_1 ... s_p]^T=\begin{pmatrix}
{s_1}_x & {s_1}_y & {s_1}_z \\
\vdots & \vdots& \vdots \\
{s_p}_x & {s_p}_y & {s_p}_z \\
\end{pmatrix}$
and p $\ge$ 6
This system is supposed to find the 6 entries of a $3\times3$ symmetric matrix.
I would like to use Matlab to find this solution.
Where is the problem ? If $p=6$, then one has a linear system of $6$ equations in the $6$ unknowns $b_{i,j}$, $i\leq j$. Write explicitly these equations. In general, the determinant of this system is non-zero and there is a unique solution.