G
gaffar
Guest
Definování matice,
<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 () \ mu \ vec (I })^{- 1) \ vec (b)" alt='3$\mathbf{X}=(\mathbf{A} \mu \mathbf{I})^{-1}\mathbf{B}' align=absmiddle>kde
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{B}' title="3 $ \ vec (b)" alt='3$\mathbf{B}' align=absmiddle>
je
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times M' title="3 $ N \ times M" alt='3$N\times M' align=absmiddle>
matice,
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{A}' title="3 $ \ vec ()" alt='3$\mathbf{A}' align=absmiddle>
je
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
matice,
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
je skalární, a
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{I}' title="3 $ \ vec (I)" alt='3$\mathbf{I}' align=absmiddle>
je
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
identity matrix.
Chtěli bychom najít
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
, Které splňují následující rovnice:<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(\mathbf{XX}^H)=c' title="3 $ tr (\ vec (XX) ^ H) = c" alt='3$tr(\mathbf{XX}^H)=c' align=absmiddle>kde
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(.)' title="3 $ tr (.)" alt='3$tr(.)' align=absmiddle>
je stopa provozovatel,
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$c' title="3 $ c" alt='3$c' align=absmiddle>
je konstantní a
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}^H' title="3 $ \ vec (X) ^ H" alt='3$\mathbf{X}^H' align=absmiddle>
je Hermitian (komplex transponovat) ze dne
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}' title="3 $ \ vec (X)" alt='3$\mathbf{X}' align=absmiddle>
.
Díky.
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\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 () \ mu \ vec (I })^{- 1) \ vec (b)" alt='3$\mathbf{X}=(\mathbf{A} \mu \mathbf{I})^{-1}\mathbf{B}' align=absmiddle>kde
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{B}' title="3 $ \ vec (b)" alt='3$\mathbf{B}' align=absmiddle>
je
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times M' title="3 $ N \ times M" alt='3$N\times M' align=absmiddle>
matice,
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{A}' title="3 $ \ vec ()" alt='3$\mathbf{A}' align=absmiddle>
je
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
matice,
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
je skalární, a
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{I}' title="3 $ \ vec (I)" alt='3$\mathbf{I}' align=absmiddle>
je
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$N\times N' title="3 $ N \ times N" alt='3$N\times N' align=absmiddle>
identity matrix.
Chtěli bychom najít
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mu' title="3 $ \ mu" alt='3$\mu' align=absmiddle>
, Které splňují následující rovnice:<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(\mathbf{XX}^H)=c' title="3 $ tr (\ vec (XX) ^ H) = c" alt='3$tr(\mathbf{XX}^H)=c' align=absmiddle>kde
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$tr(.)' title="3 $ tr (.)" alt='3$tr(.)' align=absmiddle>
je stopa provozovatel,
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$c' title="3 $ c" alt='3$c' align=absmiddle>
je konstantní a
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}^H' title="3 $ \ vec (X) ^ H" alt='3$\mathbf{X}^H' align=absmiddle>
je Hermitian (komplex transponovat) ze dne
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\mathbf{X}' title="3 $ \ vec (X)" alt='3$\mathbf{X}' align=absmiddle>
.
Díky.