Maxima Function
ModeMatrix (A,l)
Returns the matrix M such that (M^^-1).A.M=J, where J is the Jordan form of A. The Maxima list l is the codified form of the Jordan form as returned by function jordan
.
Example:
(%i1) load("diag")$ (%i2) a:matrix([2,1,2,0], [-2,2,1,2], [-2,-1,-1,1], [3,1,2,-1])$ (%i3) jordan(a); (%o3) [[- 1, 1], [1, 3]] (%i4) M: ModeMatrix(a,%); [ 1 - 1 1 1 ] [ ] [ 1 ] [ - - - 1 0 0 ] [ 9 ] [ ] (%o4) [ 13 ] [ - -- 1 - 1 0 ] [ 9 ] [ ] [ 17 ] [ -- - 1 1 1 ] [ 9 ] (%i5) is( (M^^-1).a.M = dispJordan(%o3) ); (%o5) true
Note that dispJordan(%o3)
is the Jordan form of matrix a
.
To use this function write first load("diag")
. See also and .