#LyX 1.5.3 created this file. For more info see http://www.lyx.org/ \lyxformat 276 \begin_document \begin_header \textclass article \language english \inputencoding auto \font_roman default \font_sans default \font_typewriter default \font_default_family default \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 \graphics default \paperfontsize default \papersize default \use_geometry false \use_amsmath 1 \use_esint 1 \cite_engine basic \use_bibtopic false \paperorientation portrait \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \defskip medskip \quotes_language english \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \author "" \end_header \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 \end_body \end_document