diff options
Diffstat (limited to 'anm/n1.lyx')
| -rw-r--r-- | anm/n1.lyx | 58 |
1 files changed, 28 insertions, 30 deletions
@@ -1028,52 +1028,54 @@ Existe \end_layout \end_deeper -\begin_layout Enumerate -Si -\begin_inset Formula $A$ -\end_inset +\begin_layout Standard +\begin_inset ERT +status open - es simétrica real, existe -\begin_inset Formula $O$ -\end_inset +\begin_layout Plain Layout + + +\backslash +sremember{AAlG} +\end_layout - ortogonal real con -\begin_inset Formula $O^{-1}AO$ \end_inset - diagonal. + \end_layout -\begin_deeper \begin_layout Standard -En este caso, la matriz es diagonalizable en -\begin_inset Formula $\mathbb{R}$ +Toda matriz simétrica real +\begin_inset Formula $A\in{\cal M}_{m}(\mathbb{R})$ +\end_inset + + admite una matriz ortogonal +\begin_inset Formula $P$ \end_inset + tal que +\begin_inset Formula $P^{-1}AP=P^{t}AP$ +\end_inset -\begin_inset Note Note + es diagonal. +\end_layout + +\begin_layout Standard +\begin_inset ERT status open \begin_layout Plain Layout -¿por qué? -\end_layout -\end_inset -, por lo que podemos seguir los mismos pasos que en -\begin_inset CommandInset ref -LatexCommand ref -reference "enu:unitary" -plural "false" -caps "false" -noprefix "false" +\backslash +eremember +\end_layout \end_inset - usando el producto escalar euclídeo. + \end_layout -\end_deeper \begin_layout Standard Dada \begin_inset Formula $A\in{\cal M}_{n}$ @@ -1762,7 +1764,6 @@ status open \begin_layout Plain Layout -\series bold \backslash - @@ -1776,7 +1777,6 @@ status open \begin_layout Plain Layout -\series bold \backslash - @@ -1790,7 +1790,6 @@ status open \begin_layout Plain Layout -\series bold \backslash - @@ -1804,7 +1803,6 @@ status open \begin_layout Plain Layout -\series bold \backslash - |