I'm struggling to simplify $B$ which is given by $$B=\left(A^{-1}\right)^TS\left(A^{-1}\right)$$ with S a symmetric matrix of size $2m \times 2m$ and A a matrix given by $$A=\left[\begin{matrix} Ve^{\Lambda t_i} \\ Ve^{\Lambda t_f} \end{matrix}\right]$$ where $V$ is an $m \times 2m$ matrix and $\Lambda$ is a diagonal matrix of size $2m \times 2m$.

Any ideas? For example, can we write B by using 4 blocks of size $m \times m$?

In case it helps, $A$ can also be written as $$A=\left[\begin{matrix} V_1e^{\Lambda_1 t_i} & V_2e^{\Lambda_2 t_i}\\ V_1e^{\Lambda_1 t_f} & V_2e^{\Lambda_2 t_f} \end{matrix}\right]$$ where $$V_1 = V(:,1:m)$$ $$V_2 = V(:,m+1:2m)$$ $$\Lambda_1 = \Lambda(1:m,1:m)$$ $$\Lambda_2 = \Lambda(m+1:2m,m+1:2m)$$ and of course $\Lambda_1$ and $\Lambda_2$ are diagonal matrices.


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