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Added descrpitions of functions implemented in norn_matrix.rr.

/* noro_matrix.rr $B$NMxMQNc!!(B
   $B0J2<F~NO9T$O(B tab $B$+$i;O$^$k(B.
*/

/*********************/

$BNc(B1.   $B%W%m%0%i%`$N%m!<%I(B

	load("noro_matrix.rr");

$B7k2L(B.

$B$J$7(B

$B7k2L$N@bL@(B.

	$B0J2<$N4X?t$rMQ$$$k:]$KI,MW(B.

/*********************/

$BNc(B2.   $BC10L9TNs$r@8@.$9$k(B.

	E=linalg.unit_mat(3);   	   

$B7k2L(B.

	[ 1 0 0 0 0 ]
	[ 0 1 0 0 0 ]
	[ 0 0 1 0 0 ]
	[ 0 0 0 1 0 ]
	[ 0 0 0 0 1 ]

$B7k2L$N@bL@(B.

	$B;XDj$5$l$?%5%$%:$NC10L9TNs$rJV$9(B.


/*********************/

$BNc(B3.   $B9TNs$r%i%s%@%`$K@8@.$9$k(B.

	R=linalg.random_rmat(3,4,5);

$B7k2L(B.

	[ -4 -3 2 0 ]
	[ -4 -2 -3 0 ]
	[ -2 3 -3 3 ]

$B7k2L$N@bL@(B.

	$BBh0l(B, $BBhFs0z?t$O%5%$%:(B, $B3FMWAG$O@dBPCM$,(B($BBh;00z?t(B-1)$B$N@0?t$G$"$k(B.

/*********************/

$BNc(B4. $B5U9TNs$r7W;;$9$k(B.

	A=linalg.random_mat(3,3,5);
	Inv=invmat(A);
	AI=Inv[0]/Inv[1];
	M=A*AI;

$B7k2L(B.

	A=	[ 2 0 0 0 ]
  		[ 3 5 1 0 ]
  		[ -9 -9 -1 0 ]
  		[ -5 0 0 1 ]

	Inv=[
		[ 4 0 0 0 ]
     	[ -6 -2 -2 0 ]
     	[ 18 18 10 0 ]
     	[ 20 0 0 8 ],8]


	AI=	[ 1/2 0 0 0 ]
   		[ -3/4 -1/4 -1/4 0 ]
   		[ 9/4 9/4 5/4 0 ]
   		[ 5/2 0 0 1 ]

	M=	[ 1 0 0 0 ]
  		[ 0 1 0 0 ]
  		[ 0 0 1 0 ]
  		[ 0 0 0 1 ]

$B7k2L$N@bL@(B.

	$B7k2L$O(B [Num,Den] $B$N7A$N%j%9%H$G(B, Num $B$O@0?t9TNs(B, Den $B$O@0?t$G$"$k(B.
	Num/Den $B$,5U9TNs$rI=$9(B.

/*********************/

$BNc(B5.  $B9TNs$N:G>.B?9`<0$r7W;;$9$k(B.

	A=linalg.random_rmat(3,3,5);
	M=linalg.minipoly_mat(A);

$B7k2L(B.

	A=	[ -4 3 3 ]
  		[ 1 2 3 ]
  		[ 0 4 -3 ]

	M=x^3+5*x^2-17*x-93

$B7k2L$N@bL@(B.

	f(A)=0 $B$H$J$k:G>.<!?t$NB?9`<0(B f(x) $B$rJV$9(B. deg(f) $B$,(B A $B$N%5%$%:(B
	$B$h$j>.$5$$$3$H$b$"$jF@$k(B.

/*********************/

$BNc(B6.   $B9TNs(BA$B$N3K$r7W;;$9$k(B.

	A=linalg.random_rmat(3,5,5);
	Ker=linalg.compute_kernel(A);

$B7k2L(B.

	A=	[ 4 -3 -4 -4 -4 ]
  		[ 3 3 0 -1 3 ]
  		[ -3 -3 0 1 -3 ]

	Ker=[[[ 2 0 0 3 -1 ],0],[[ 0 16 0 3 -15 ],1],[[ 0 0 4 -3 -1 ],2]]

$B7k2L$N@bL@(B.

	[[v1,p1],[v2,p2],...] $B$N7A$N%j%9%H$,JV$k(B. vi $B$O%5%$%:$,(B A $B$NNs?t$HEy$7(B
	$B$$%Y%/%H%k$G(B, [v1,v2,...] $B$,(B Ker(A) $B$N0lAH$N4pDl$G$"$k(B. pi $B$O(B vi $B$NMWAG(B
	$B$r:8$+$i$_$F(B, $B:G=i$N(B 0 $B$G$J$$MWAG$N0LCV$r<($9(B. $B:G$b:8$r(B 0 $B$H$9$k(B.

/*********************/

$BNc(B7.   $B9TNs$NA|$r7W;;$9$k(B.

	A=linalg.random_rmat(3,5,5);
	Im=linalg.compute_image(A);

$B7k2L(B.

	A=	[ 1 1 1 -1 4 ]
  		[ -3 3 2 -4 -3 ]
  		[ 3 3 0 1 4 ]

	Im=[[[ 1 -3 3 ],0,(1)*<<0>>],
    	[[ 0 6 0 ],1,(1)*<<1>>+(-1)*<<0>>],
    	[[ 0 0 -18 ],2,(6)*<<2>>+(-5)*<<1>>+(-1)*<<0>>]]

$B7k2L$N@bL@(B.

	[[v1,p1,g1],[v2,p2,g2],...] $B$N7A$N%j%9%H$rJV$9(B. vi $B$O%Y%/%H%k$G(B
	[v1,v2,...] $B$,(B Im(A) $B$N0lAH$N4pDl$G$"$k(B.  pi $B$O(B vi $B$NMWAG$r:8$+$i$_$F(B, 
	$B:G=i$N(B 0 $B$G$J$$MWAG$N0LCV$r<($9(B. $B:G$b:8$r(B 0 $B$H$9$k(B. gi $B$O(B, vi $B$,(B
	$B$b$H$N9TNs$NNs$+$i$I$N$h$&$K@8@.$5$l$F$$$k$+$r<($9J,;6B?9`<0$G$"$k(B.
	$BNc$($P>e$NNc$G$O(B, [0 6 0] $B$O(B ($BBh(B 1 $BNs(B-$BBh(B 0 $BNs(B) $B$KEy$7$$$3$H$,J,$+$k(B.

/*********************/

$BNc(B8.   $B9TNs(BA$B$N(BJordan $BI8=`7A$r7W;;$9$k(B.

	A=newmat(4,4,[[2,0,0,0],[3,5,1,0],[-9,-9,-1,0],[-5,0,0,1]]);
	B=linalg.jordan_canonical_form(A);
	P=B[0];
	L=invmat(P); PI=L[0]/L[1];
	S=PI*A*P;

$B7k2L(B.

	B=[
		[ 0 1 1 0 ]
		[ 3 0 0 0 ]
		[ -9 0 -3 0 ]
		[ 0 -5 -5 1 ],
		[[2,2,1],[2,1,1],[1,1,1]],[]]

	S=	[ 2 1 0 0 ]
  		[ 0 2 0 0 ]
  		[ 0 0 2 0 ]
  		[ 0 0 0 1 ]

$B7k2L$N@bL@(B.

	$B7k2L$O(B [P,[[e1,m1,j1],[e2,m2,j2],...],DefiningIdeal] $B$N7A$N%j%9%H$G$"$k(B.
	P $B$OJQ499TNs(B, $B$9$J$o$A(B P^(-1)AP $B$,(B Jordan $BI8=`7A$K$J$k9TNs$rI=$9(B.
	$B<!$NMWAG$O(B Jordan $BI8=`7A$r9=@.$9$k(B Jordan $B%V%m%C%/$N%j%9%H$G$"$k(B.
	[ei,mi,ji] $B$O(B, $B8GM-CM(B ei, $B%5%$%:(B mi $B$N(B Jordan $B%V%m%C%/$,(B ji $B8D$"$k$3$H(B
	$B$r<($9(B. $BF@$i$l$?(B P $B$K$h$j7W;;$9$k$H(B, $B3N$+$K$=$&$J$C$F$$$k$3$H$,>e$N(B
	$BNc$GJ,$+$k(B. $B0lHL$K$O(B, $B8GM-CM$OBe?tE*?t$H$J$k(B. $B$3$N>l9g(B, $B8GM-CM$r(B
	$BI=$9ITDj85$,I,MW$J$@$1@8@.$5$l(B, $B0lHL8GM-%Y%/%H%k(B (P $B$NNs%Y%/%H%k(B)
	$B$O$=$l$i$GI=8=$5$l$k(B. DefiningIdeal $B$O$=$l$i$NITDj85$rDj5A$9$k(B
	$B%$%G%"%k$G$"$k(B.