Article View: fj.sci.math
Article #13545Re: How to solve the LMI of symmetric matrix's semidefinite condition?
From: Tsukamoto, Chiaki
Date: Thu, 05 Sep 1996 00:00
Date: Thu, 05 Sep 1996 00:00
76 lines
2761 bytes
2761 bytes
$B9)A!Bg$NDMK\$G$9(B. In article <50ln1e$514@ces.ces.kyutech.ac.jp> zhang@ces.ces.kyutech.ac.jp (Hong Zhang) writes: > $B$3$N>l9g$OD>8r9TNs(B P$B$O0l0U$KDj$^$k$+$i!"5a$a$?$N$OBP>NH>(B > $B@5Dj9TNs&!B2$NCf$N$?$@$N0l$D$G$"$k$H;W$$$^$9!#(B $BD>8r9TNs(B P $B$O0l0U$K$ODj$^$j$^$;$s$,(B, $BJ}Dx<0$r=q$-D>$9$K$O>r7o(B P X = e_1, P B = a e_1 + b e_2 $B$r(B $BK~$?$9$b$N$r0l$D<h$C$F8GDj$9$l$PNI$/(B, $BBP>NH>@5DjCM9TNs(B A $B$NA4BN$r5a$a$k$3$H$O(B $BBP>NH>@5DjCM9TNs(B C $B$NA4BN$r5a$a$k$3$H$K5"Ce$7$^$9(B. $B$J$*(B, P $B$N<h$jJ}$NITDj@-$rMxMQ$7$F(B C $B$N7A$r$b$&>/$7@)8B$7(B, $BH>@5DjCM@-$rH=Dj$7$d$9$/=PMh$?$j$9$k$H;W$$$^$9$,(B, $B$=$l$O$48&5f2<$5$$(B. > $B$^$?(B n $B<!85$N(B > $BLdBj$K3HD%$9$k$H!">e5-$N(BMatrix$B$NCf$N(B*$B$H$3$m$NCM$OG!2?$KDj$a(B > $B$k$+$K$F!"MF0W$G$O$J$$$H;W$C$F!"G!2?$G$7$g$&!#(B n = 4 $B$G@5DjCM$N>r7o$G$b$N$r9M$($k$J$i$P(B a b 0 0 b c d e 0 d f g 0 e g h $B$G(B c, d, e, f, g, h $B$r(B (a > 0 $B$O2>Dj$7$F$*$$$F(B) |a b| = a c - b^2 > 0, |b c| |a b 0| |b c d| = (a c - b^2) e - a d^2 > 0, |0 d e| |a b 0 0| |b c d e| > 0, |0 d f g| |0 e g h| $B$rK~$?$9$h$&$K<h$k$3$H$,I,MW==J,>r7o$H$J$k$H$$$&0UL#$G(B $B0l$D$N2rK!$K$O$J$j$^$9(B. $BH>@5DjCM$@$H>e$N(B ">" $B$rEy9fIU$-$KJQ$($?$b$N$O(B $BI,MW>r7o$rM?$($^$9$,(B, $B==J,>r7o$K$O$J$j$^$;$s(B. $B$J$*(B, $B@h$K=R$Y$?$h$&$K(B P $B$K$D$$$F$N(B 1 0 0 0 0 1 0 0 0 0 p q 0 0 r s p q $B$OD>8r9TNs(B r s $B$H$$$&7A$ND>8r9TNs$NG$0U@-$rMxMQ$9$k$H(B g = 0, f $B$H(B h $B$H$OHsIi(B, $B$r2>Dj$7$F9M$($k$3$H$,=PMh$kLu$G$9(B. $B=j4|$N2rEz$rF@$k$3$H$,=PMh$k$+$I$&$+$OJ,$+$j$^$;$s$,(B $B>e$N$h$&$J9M;!$+$i=PH/$5$l$F$OG!2?$G$7$g$&$+(B. > LMI $B$H$O(B Linear Matrix Inequalities$B$N=L<L$G$9!#(BLMI$BM}O@$O(B > $B@)8f%7%9%F%`$N%Q%i%a!<%?@_7W$K$h$/;H$o$l$F$$$k$h$&$G$9!#(B \rho $B$,AH$_9~$^$l$F$$$k$H$3$m$,!VITEy<0!W$J$N$G$7$g$&$M(B. $B6qBNE*$J>u67$+$i$N@)8B$,$"$k$J$i(B, $B$b$&>/$7OC$,?J$`$+$b$7$l$^$;$s(B. $B2?$+LLGr$=$&$JOCBj$,$"$l$P$4>R2p$/$@$5$$(B. -- $BDMK\@i=)(B@$B1~MQ?t3X(B.$B9bJ,;R3X2J(B.$BA!0]3XIt(B.$B5~ET9)7]A!0]Bg3X(B Tsukamoto, C. : chiaki@ipc.kit.ac.jp
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X-Google-Language: Japanese,JIS X-Google-Thread: f4956,22a531ac63328363 X-Google-Attributes: gidf4956,public From: g52997@sakura.kudpc.kyoto-u.ac.jp (Tsukamoto, Chiaki) Subject: Re: How to solve the LMI of symmetric matrix's semidefinite condition? Date: 1996/09/05 Message-ID: <50mrk1$gg3@sakura.kudpc.kyoto-u.ac.jp> X-Deja-AN: 180078850 references: <50lg4f$7vk@sakura.kudpc.kyoto-u.ac.jp> organization: Kyoto Institute of Technology, Kyoto 606, JAPAN reply-to: chiaki@ipc.kit.ac.jp newsgroups: fj.sci.math