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SciMax Toolbox >> ModeMatrix

ModeMatrix

Maxima Function

Calling Sequence

ModeMatrix (A,l)

Description

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 .

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