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Article #14153

[Q] calculus for linear independence..?

#14153
From: Kentaro Kondo
Date: Sat, 11 Nov 1995 00:00
31 lines
1687 bytes
$B@hF|$O!"0l<!FHN)$NH=Dj$N7W;;J}K!$K$D$$$F>pJs$r$$$?$@$-!"(B
$B$I$&$b$"$j$,$H$&$4$6$$$^$7$?!#(B

$B$5$F!"$3$l$r1~MQ$7$F!"(B
$B0J2<$N$h$&$K!"8=:_9M$($F$$$kLdBj$r2r$$$F$_$^$7$?!#(B


3 $B<oN`$N%Y%/%?!<$N(B Hermitian $B1i;;;R$rAH$_9g$o$;$F!"(B
$B0J2<$N#3$D(B F1, F2, F3 $B$r:n$C$?$H$-!"(B
 F1 = ( Kx*Sy - Ky*Sx ) * ( Lx*Lx + Ly*Ly )
 F2 = ( Kx*Ly - Ky*Lx ) * ( Sx*Lx + Sy*Ly ) + Hermitian conjugate
 F3 = ( Kx*Lx + Ky*Ly ) * ( Sx*Ly - Sy*Lx ) + Hermitian conjugate
    $B$D$^$j!"(BFi $B":(B $B#V(B = ( Kx, Ky ) @ ( Sx, Sy ) @ ( Lx*Lx, Ly*Ly, LxLy+LyLx )
$B$3$N#3$D$,0l<!FHN)$+$I$&$+$rD4$Y$k$?$a$K$O!"Fb@Q(B(?)$B$+$i$J$k9TNs(B
                           4   4  -4
 ( Mij ) = ( <Fi,Fj> ) =   4  10   2
                          -4   2  10
$B$r8+$l$P$h$$!#!J(B det( Mij ) = 0 $B$K$J$k!K(B
$B#3$D$N$&$A$I$l$+#1$D$r=|$1$P!";D$j$N#2$D$O0l<!FHN)$K$J$k$3$H$,J,$+$k!#(B

$B#P#S!%$h$C$F!"(Bz $B<42sE>$KBP$7$FITJQ$J(B Hermitian operator $B$O!"(B
$B<B78?t(B C1, C2 $B$rMQ$$$F!"(B
         C1 * F1 + C2 * F2
$B$HI=$;$k$3$H$,$o$+$j$^$7$?!%!%!#(B


$B#P#S#2!%0J>e$N$h$&$J1~MQ$GNI$$$G$7$g$&$+!%!%!)(B

---------------------------------------------
     Kentaro Kondo (kkondo@flab.fujitsu.co.jp)
     Fujitsu Labs. Ltd.
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Message-ID: <kkondo-1111951845560001@164.70.23.81>
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X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,1b9a21ce2696d190,start
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From: kkondo@flab.fujitsu.co.jp (Kentaro Kondo)
Subject: [Q] calculus for linear independence..?
Date: 1995/11/11
Message-ID: <kkondo-1111951845560001@164.70.23.81>
X-Deja-AN: 119148806
sender: news@akashi.flab.fujitsu.co.jp
organization: Fujitsu Labs. Ltd.
newsgroups: fj.sci.math