load("diag.mc")$
a:matrix([2,0,0,0,0,0,0,0],
       	 [1,2,0,0,0,0,0,0],
	 [-4,1,2,0,0,0,0,0],
	 [2,0,0,2,0,0,0,0],
	 [-7,2,0,0,2,0,0,0],
	 [9,0,-2,0,1,2,0,0],
	 [-34,7,1,-2,-1,1,2,0],
	 [145,-17,-16,3,9,-2,0,3])$
a1:matrix([2,1,0,0,0,0],
       	  [-1,4,0,0,0,0],
	  [-1,1,2,1,0,0],
	  [-1,1,-1,4,0,0],
	  [-1,1,-1,1,3,0],
	  [-1,1,-1,1,1,2])$
a2:matrix([0,1,0],
       	  [0,0,1],
	  [1,-3,3])$
a3:matrix([0,1,2],
       	  [0,0,0],
	  [0,0,0])$
a4:matrix([3,1,0,0],
       	  [-4,-1,0,0],
	  [7,1,2,1],
	  [-17,-6,-1,0])$
a5:matrix([2,1,2,0],
       	  [-2,2,1,2],
	  [-2,-1,-1,1],
	  [3,1,2,-1])$
	 
b1:matrix([0,0,1,1,1],
       	  [0,0,0,1,1],
	  [0,0,0,0,1],
	  [0,0,0,0,0],
	  [0,0,0,0,0])$
b2:matrix([0,1,0],
	  [0,0,1],
	  [-1,-3,-3])$
/* jordan form */
a;
jordan(a);
dispJordan(%);
mm:ModeMatrix(a,jordan(a));
(mm^^-1).a.mm;
a1;
jordan(a1);
dispJordan(%);
mm:ModeMatrix(a1,jordan(a1));
(mm^^-1).a1.mm;
a2;
jordan(a2);
dispJordan(%);
mm:ModeMatrix(a2,jordan(a2));
(mm^^-1).a2.mm;
a3;
jordan(a3);
dispJordan(%);
mm:ModeMatrix(a3,jordan(a3));
(mm^^-1).a3.mm;
a4;
jordan(a4);
dispJordan(%);
mm:ModeMatrix(a4,jordan(a4));
(mm^^-1).a4.mm;
a5;
jordan(a5);
dispJordan(%);
mm:ModeMatrix(a5,jordan(a5));
(mm^^-1).a5.mm;

/*diag ,JF example */
minimalPoly(jordan(a));
JF(3,5);
diag([JF(1,5),2*t,JF(3,2)]);

/*matrix function*/
mat_function(exp,t*b2);
ratsimp(%);
mat_function(exp,t*b1);
minimalPoly(jordan(b1));
ident(5)+t*b1+1/2*(t^2)*b1^^2;
mat_function(exp,%i*t*b1);
mat_function(cos,t*b1)+%i*mat_function(sin,t*b1);
fpow(x):=block([k],declare(k,integer),x^k);
mat_function(fpow,a1);
/* please try mat_function(fpow,a)and ratsimp */