I have matrix difference equation (Riccati equation): $ X(k+1) = Q + F\left(I - X(k)H^{T}\left(HX(k)H^{T} + R\right)^{-1}H\right)X(k)F^{T}. $ I have to work on the trace of this matrix.
Is there someway to write $t(k+1) = \operatorname{tr} \biggr(X(k+1)\biggr)$ as a function of $t(k) = \operatorname{tr}\biggr(X(k)\biggr)$? I mean, $t(k+1) = f\biggr(t(k)\biggr)$.
Some suggestions?
Addition:
I forgot that all involved matrices are symmetric and semidefinite positive.