I am trying to create a matrix like the following
where notice that I envision it as a 4x4 matrix, with 4 blocks, one 1x1 block, one 3x1 block, one 1x3 block, and one 3x3 matrix. My confusion in writing this is in having the matrix by partitioned according to the above decomposition, BUT with only one element written in each block.
The only thing I know how to do is to write this as a 2x2 matrix which is not satisfying
\begin{align} G^\mu{}_\nu &= \frac{\partial x ' {}^\mu}{\partial x^\nu} \\ \notag &= \left( \begin{array}{c|c} \frac{\partial x ' {}^0}{\partial x^0} & \frac{\partial x ' {}^0}{\partial x^i} \\ \hline \frac{\partial x ' {}^i}{\partial x^0} & \frac{\partial x ' {}^i}{\partial x^j} \end{array} \right) \\ \notag &= \left( \begin{array}{c|c} 1 & 0 \\ \hline v^i & R^i{}_j \end{array} \right) \end{align} Any tips on how to create a 4x4 matrix with only one written element in a 3x3 (3x1, 1x3) block?

