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version 1.2, 2002/08/08 08:56:32 version 1.3, 2002/08/14 09:17:58
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 @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Matrix-ja.texi,v 1.1 2002/07/29 02:56:27 takayama Exp $  
 @node Matrix operations (library by Okutani),,, Top  
 @chapter Matrix operations (library by Okutani)  
 $B%U%!%$%k(B @file{gr}, @file{Matrix} $B$,I,MW$G$9(B.  
   
 Yukio Okutani $B;a$K$h$k(B Risa/Asir $B8@8l$G=q$+$l$?9TNs7W;;MQ$N%i%$%V%i%j$G$9(B.  @node $B9TNs(B($BI8=`?t3XH!?t(B),,, Top
 $B$9$Y$F$N4X?tL>$O(B omatrix_ $B$G;O$^$j$^$9(B.  @chapter $B9TNs(B($BI8=`?t3XH!?t(B)
   
 @menu  @include matrix-auto-ja.texi
 * omatrix_1::  
 * omatrix_diag::  
 * omatrix_trans::  
 * omatrix_inverse::  
 * omatrix_solve::  
 * omatrix_kernel::  
 @end menu  
   
 @node omatrix_1,,, Matrix operations (library by Okutani)  
 @subsection @code{omatrix_1}  
 @findex omatrix_1  
 @table @t  
 @item omatrix_1(@var{N})  
 ::  @var{N} $B<!C10L9TNs$r@8@.$7$^$9(B.  
 @end table  
 @table @var  
 @item return  
 $B9TNs(B  
 @item N  
 $B@0?t(B  
 @end table  
 @itemize @bullet  
 @item  @code{omatrix_1}$B$NNc(B.  
 @end itemize  
 @example  
 [297] omatrix_1(1);  
 [ 1 ]  
   
 [298] omatrix_1(2);  
 [ 1 0 ]  
 [ 0 1 ]  
   
 [299] omatrix_1(3);  
 [ 1 0 0 ]  
 [ 0 1 0 ]  
 [ 0 0 1 ]  
 @end example  
   
 @node omatrix_diag,,, Matrix operations (library by Okutani)  
 @subsection @code{omatrix_diag}  
 @findex omatrix_diag  
 @table @t  
 @item omatrix_diag(@var{L})  
 ::  $B%j%9%H(B @var{L} $B$NMWAG$rBP3Q@.J,$H$9$kBP3Q9TNs$r@8@.$7$^$9(B.  
 @end table  
 @table @var  
 @item return  
 $B9TNs(B  
 @item L  
 $B%j%9%H(B  
 @end table  
 @itemize @bullet  
 @item  @code{omatrix_diag}$B$NNc(B.  
 @end itemize  
 @example  
 [301] omatrix_diag([1,2,3]);  
 [ 1 0 0 ]  
 [ 0 2 0 ]  
 [ 0 0 3 ]  
   
 [302] omatrix_diag([a,b,c]);  
 [ a 0 0 ]  
 [ 0 b 0 ]  
 [ 0 0 c ]  
 @end example  
   
 @node omatrix_trans,,, Matrix operations (library by Okutani)  
 @subsection @code{omatrix_trans}  
 @findex omatrix_trans  
 @table @t  
 @item omatrix_trans(@var{A})  
 ::  $B9TNs(B @var{A} $B$NE>CV9TNs$r5a$a$^$9(B.  
 @end table  
 @table @var  
 @item return  
 $B9TNs(B  
 @item A  
 $B9TNs(B or $B%j%9%H(B  
 @end table  
 @itemize @bullet  
 @item  @code{omatrix_trans}$B$NNc(B.  
 @end itemize  
 @example  
 [303] omatrix_trans([[a,b],[c,d]]);  
 [ a c ]  
 [ b d ]  
   
 [304] omatrix_trans([[1,2,3],[4,5,6],[7,8,9]]);  
 [ 1 4 7 ]  
 [ 2 5 8 ]  
 [ 3 6 9 ]  
 @end example  
   
 @node omatrix_inverse,,, Matrix operations (library by Okutani)  
 @subsection @code{omatrix_inverse}  
 @findex omatrix_inverse  
 @table @t  
 @item omatrix_inverse(@var{A})  
 ::  $B9TNs(B @var{A} $B$N5U9TNs$r5a$a$^$9(B.  
 @end table  
 @table @var  
 @item return  
 $B9TNs(B  
 @item A  
 $B9TNs(B or $B%j%9%H(B  
 @end table  
 @itemize @bullet  
 @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.  
 @item $B0[$J$k%"%k%4%j%:%`$rMQ$$$F5U9TNs$r7W;;$9$k(B  
 @code{omatrix_inverse2}, @code{omatrix_inverse3}  
 $B$b$"$k(B.  
 @item @code{omatrix_inverse}$B$NNc(B.  
 @end itemize  
 @example  
 [309] omatrix_inverse([[1,1],[1,2]]);  
 [ 2 -1 ]  
 [ -1 1 ]  
   
 [310] omatrix_inverse([[a,b],[c,d]]);  
 [ (d)/(d*a-c*b) (-b)/(d*a-c*b) ]  
 [ (-c)/(d*a-c*b) (a)/(d*a-c*b) ]  
 @end example  
   
 @node omatrix_solve,,, Matrix operations (library by Okutani)  
 @subsection @code{omatrix_solve}  
 @findex omatrix_solve  
 @table @t  
 @item omatrix_solve(@var{A},@var{X},@var{Y})  
 ::  @code{omatrix_solve}$B$OJ}Dx<0(B A*X=Y $B$N2r$r5a$a$^$9(B.  
 @end table  
 @table @var  
 @item return  
 $B%j%9%H(B  
 @item A  
 $B9TNs(B or $B%j%9%H(B  
 @item X  
 $B%Y%/%H%k(B or $B%j%9%H(B  
 @item Y  
 $B%Y%/%H%k(B or $B%j%9%H(B  
 @end table  
 @itemize @bullet  
 @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.  
 @item  @code{omatrix_solve}$B$NNc(B.  
 @end itemize  
 @example  
 [376] omatrix_solve([[1,-1],[2,3]],[x,y],[1,1]);  
 [[x,4/5],[y,-1/5]]  
   
 [377] omatrix_solve([[a,b],[c,d]],[x,y],[1,1]);  
 [[x,(-b+d)/(d*a-c*b)],[y,(a-c)/(d*a-c*b)]]  
 @end example  
   
 @node omatrix_kernel,,, Matrix operations (library by Okutani)  
 @subsection @code{omatrix_kernel}  
 @findex omatrix_kernel  
 @table @t  
 @item omatrix_kernel(@var{A})  
 ::  @code{omatrix_kernel}$B$O9TNs(B A $B$N(B kernel $B$N4pDl$r5a$a$^$9(B.  
 @end table  
 @table @var  
 @item return  
 $B%j%9%H(B  
 @item A  
 $B9TNs(B or $B%j%9%H(B  
 @end table  
 @itemize @bullet  
 @item $B9TNs(B @var{A} $B$N@.J,$OM-M}?t(B or $BB?9`<0(B.  
 @item  @code{omatrix_kernel}$B$NNc(B.  
 @end itemize  
 @example  
 [383] omatrix_kernel([[1,2,3,4],[1,0,1,0]]);  
 [2,[[1,0,-1,1/2],[0,1,0,-1/2]]]  
   
 [384] omatrix_kernel([[1,2,3,4],[1,0,1,0],[0,0,0,1]]);  
 [1,[[1,1,-1,0]]]  
 @end example  
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