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@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Matrix.texi,v 1.2 1999/11/29 05:01:42 okutani Exp $
@node Matrix operations,,, $B$=$NB>$NH!?t(B
@section Matrix operations
$B%U%!%$%k(B @file{gr} $B$,I,MW$G$9(B.
@menu
* mat_1::
* mat_diag::
* mat_trans::
* mat_inverse::
* mat_solve::
* mat_kernel::
@end menu

@node mat_1,,, Matrix operations
@subsection @code{mat_1}
@findex mat_1
@table @t
@item mat_1(@var{N})
::  @var{N} $B<!C10L9TNs$r@8@.$7$^$9(B.
@end table
@table @var
@item return
$B9TNs(B
@item N
$B@0?t(B
@end table
@itemize @bullet
@item  @code{mat_1}$B$NNc(B.
@end itemize
@example
[297] mat_1(1);
[ 1 ]

[298] mat_1(2);
[ 1 0 ]
[ 0 1 ]

[299] mat_1(3);
[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]
@end example

@node mat_diag,,, Matrix operations
@subsection @code{mat_diag}
@findex mat_diag
@table @t
@item mat_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
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{mat_diag}$B$NNc(B.
@end itemize
@example
[301] mat_diag([1,2,3]);
[ 1 0 0 ]
[ 0 2 0 ]
[ 0 0 3 ]

[302] mat_diag([a,b,c]);
[ a 0 0 ]
[ 0 b 0 ]
[ 0 0 c ]
@end example

@node mat_trans,,, Matrix operations
@subsection @code{mat_trans}
@findex mat_trans
@table @t
@item mat_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 $B%j%9%H(B
@end table
@itemize @bullet
@item  @code{mat_trans}$B$NNc(B.
@end itemize
@example
[303] mat_trans([[a,b],[c,d]]);
[ a c ]
[ b d ]

[304] mat_trans([[1,2,3],[4,5,6],[7,8,9]]);
[ 1 4 7 ]
[ 2 5 8 ]
[ 3 6 9 ]
@end example

@node mat_inverse,,, Matrix operations
@subsection @code{mat_inverse}
@findex mat_inverse
@table @t
@item mat_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 $BB?9`<0(B.
@item @code{mat_inverse}$B$NNc(B.
@end itemize
@example
[309] mat_inverse([[1,1],[1,2]]);
[ 2 -1 ]
[ -1 1 ]

[310] mat_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 mat_solve,,, Matrix operations
@subsection @code{mat_solve}
@findex mat_solve
@table @t
@item mat_solve(@var{A},@var{X},@var{Y})
::  @code{mat_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 $BB?9`<0(B.
@item  @code{mat_solve}$B$NNc(B.
@end itemize
@example
[376] mat_solve([[1,-1],[2,3]],[x,y],[1,1]);
[[x,4/5],[y,-1/5]]

[377] mat_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 mat_kernel,,, Matrix operations
@subsection @code{mat_kernel}
@findex mat_kernel
@table @t
@item mat_kernel(@var{A})
::  @code{mat_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 $BB?9`<0(B.
@item  @code{mat_kernel}$B$NNc(B.
@end itemize
@example
[383] mat_kernel([[1,2,3,4],[1,0,1,0]]);
[2,[[1,0,-1,1/2],[0,1,0,-1/2]]]

[384] mat_kernel([[1,2,3,4],[1,0,1,0],[0,0,0,1]]);
[1,[[1,1,-1,0]]]
@end example