G
Gaffar
Guest
Het definiëren van een matrix,
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}' title="3 $ \ vec (X)" alt='3$\mathbf{X}' align=absmiddle>
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}=(\mathbf{A} \mu \mathbf{I})^{-1}\mathbf{B}' title="3 $ \ vec (X) = (\ vec (A) \ mu \ vec (I })^{- 1) \ vec (B)" alt='3$\mathbf{X}=(\mathbf{A} \mu \mathbf{I})^{-1}\mathbf{B}' align=absmiddle>waar
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{B}' title="3 $ \ vec (B)" alt='3$\mathbf{B}' align=absmiddle>
is
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times M' title="3 $ N \ times M" alt='3$N\times M' align=absmiddle>
matrix
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{A}' title="3 $ \ vec (A)" alt='3$\mathbf{A}' align=absmiddle>
is
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
matrix
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
is een scalair, en
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{I}' title="3 $ \ vec (I)" alt='3$\mathbf{I}' align=absmiddle>
is
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
identiteit matrix.
We willen vinden
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
, Voldoet aan de volgende vergelijking:<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(\mathbf{XX}^H)=c' title="3 $ tr (\ vec (XX) ^ H) = c" alt='3$tr(\mathbf{XX}^H)=c' align=absmiddle>waar
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(.)' title="3 $ tr (.)" alt='3$tr(.)' align=absmiddle>
trace is exploitant
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$c' title="3 $ c" alt='3$c' align=absmiddle>
is een constante, en
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}^H' title="3 $ \ vec (X) ^ H" alt='3$\mathbf{X}^H' align=absmiddle>
de Hermitische (complexe omzetting) van
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}' title="3 $ \ vec (X)" alt='3$\mathbf{X}' align=absmiddle>
.
Bedankt.
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}' title="3 $ \ vec (X)" alt='3$\mathbf{X}' align=absmiddle>
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}=(\mathbf{A} \mu \mathbf{I})^{-1}\mathbf{B}' title="3 $ \ vec (X) = (\ vec (A) \ mu \ vec (I })^{- 1) \ vec (B)" alt='3$\mathbf{X}=(\mathbf{A} \mu \mathbf{I})^{-1}\mathbf{B}' align=absmiddle>waar
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{B}' title="3 $ \ vec (B)" alt='3$\mathbf{B}' align=absmiddle>
is
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times M' title="3 $ N \ times M" alt='3$N\times M' align=absmiddle>
matrix
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{A}' title="3 $ \ vec (A)" alt='3$\mathbf{A}' align=absmiddle>
is
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
matrix
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
is een scalair, en
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{I}' title="3 $ \ vec (I)" alt='3$\mathbf{I}' align=absmiddle>
is
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
identiteit matrix.
We willen vinden
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
, Voldoet aan de volgende vergelijking:<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(\mathbf{XX}^H)=c' title="3 $ tr (\ vec (XX) ^ H) = c" alt='3$tr(\mathbf{XX}^H)=c' align=absmiddle>waar
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(.)' title="3 $ tr (.)" alt='3$tr(.)' align=absmiddle>
trace is exploitant
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$c' title="3 $ c" alt='3$c' align=absmiddle>
is een constante, en
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}^H' title="3 $ \ vec (X) ^ H" alt='3$\mathbf{X}^H' align=absmiddle>
de Hermitische (complexe omzetting) van
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}' title="3 $ \ vec (X)" alt='3$\mathbf{X}' align=absmiddle>
.
Bedankt.