root/library/bdm/math/KF_chol.lyx @ 433

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\begin_body

\begin_layout Standard
Forl lower triangular matrices
\begin_inset Formula \[
\left[\begin{array}{ccc}
R^{0.5} & CP_{t|t-1}^{0.5} & 0\\
0 & AP_{t|t-1}^{0.5} & Q^{0.5}\end{array}\right]<\mathrm{orth.oper.}>=\left[\begin{array}{ccc}
R_{y}^{0.5} & 0 & 0\\
AK & P_{t+1|t}^{0.5} & 0\end{array}\right]\]

\end_inset

After transpose (for upper triangular matrices):
\begin_inset Formula \[
\left[\begin{array}{cc}
R^{0.5}\\
P_{t|t-1}^{0.5}C' & P_{t|t-1}^{0.5}CA'\\
 & Q^{0.5}\end{array}\right]<\mathrm{orth.oper.}>=\left[\begin{array}{cc}
R_{y}^{0.5} & KA'\\
 & P_{t+1|t}^{0.5}\\
\\\end{array}\right]\]

\end_inset


\end_layout

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