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Article #13542

Re: How to solve the LMI of symmetric matrix's semidefinite condition?

#13542
From: Tsukamoto, Chiaki
Date: Thu, 05 Sep 1996 00:00
42 lines
2162 bytes
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In article <50ja0p$pqo@ces.ces.kyutech.ac.jp>
zhang@ces.ces.kyutech.ac.jp (Hong Zhang) writes:
>   $B<ALd$O<!$N@~7AJ}Dx<0(B $B&!&6(B=$B&Q&"$rK~B-$9$k9TNs&!(B($B&!$OBP>N!"H>@5Dj(B
> $B9TNs(B)$BB2$rG!2?$K5a$a$k$+$H$N$3$H$G$9!#$?$@$7!"&6$H&"$O%Y%/%H%k!"&Q(B
> $B$OJQ?t$G!"$7$+$b&Q(B>=0$B$G$9!#(B

X $B$ONm%Y%/%H%k$G$O$J$$$G$9$M(B. $BN>JU$r%9%+%i!<G\$7$F(B
X $B$ND9$5$O(B 1$B$G$"$k$H$7$^$7$g$&(B.

$BD>8r9TNs(B  P $B$r(B P X = e_1, P B = a e_1 + b e_2 $B$H(B
$B$J$k$h$&$KA*$S$^$9(B. $B$3$3$G(B e_1, e_2, ... , e_n $B$O(B
$BI8=`4pDl$G$9(B. P $B$NE>CV9TNs$r(B  P^* $B$H$7$^$9(B.
$B>e$NJ}Dx<0$O(B P A X = \rho P B $B$HF1CM$G$9(B.
$B99$K=q$-D>$9$H(B, P A P^* P X = P A P^* e_1 = \rho (a e_1 + b e_2)
$B$H$J$j$^$9(B. $B$3$3$G(B  P A P^* = C $B$H$9$l$P(B  A = P^* C P $B$G$"$j(B,

 C e_1 = \rho (a e_1 + b e_2)

$B$rK~$?$9BP>NH>@5DjCM9TNs$r5a$a$k$3$H$K5"Ce$7$^$9(B. C $B$O(B

a b 0 0
b c * *
0 * * *
0 * * *

$B$N7A$NBP>NH>@5DjCM9TNs$N(B \rho $BG\$H$$$&Lu$G$9(B.
 ($BC"$7(B, \rho > 0.  \rho = 0 $B$@$H>/$70c$C$F$-$^$9(B.)
$BH>@5DjCM$N>r7o$O$A$g$C$HLq2p$G$9$M(B. $B@5DjCM$J$i4JC1$G$9$,(B.
$BI,MW>r7o$O(B a = (X, B)  ($BFb@Q(B) $B$,HsIi$H$+(B a c - b^2 $B$,(B
$BHsIi$H$+$,=P$F$-$^$9(B.

>  $B$3$l$O9TNs&!$K4X$9$k(BLMI$BLdBj$J$N$G!"?t3XE*$J5a$aJ}$O$"$k$N$G$7$g(B
> $B$&$+(B? $B$^$?LdBj2r7h$KEv$?$j!"%R%s%H$N$"$k;29MJ88%$dK\$,$"$j$^$7$?(B
> $B$i!"8f>R2p2<$5$$!#(B

LMI $B$H$O2?$G$7$g$&$+(B.
-- 
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Tsukamoto, C. : chiaki@ipc.kit.ac.jp
Technical Details
Message-ID: <50lg4f$7vk@sakura.kudpc.kyoto-u.ac.jp>
Path: arc1-ca.pugleaf.net!unknown!not-for-mail
References: <50ja0p$pqo@ces.ces.kyutech.ac.jp>

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X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,22a531ac63328363,start
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From: g52997@sakura.kudpc.kyoto-u.ac.jp (Tsukamoto, Chiaki)
Subject: Re: How to solve the LMI of symmetric matrix's semidefinite condition?
Date: 1996/09/05
Message-ID: <50lg4f$7vk@sakura.kudpc.kyoto-u.ac.jp>
X-Deja-AN: 179199076
references: <50ja0p$pqo@ces.ces.kyutech.ac.jp>
organization: Kyoto Institute of Technology, Kyoto 606, JAPAN
newsgroups: fj.sci.math