*To*: mathgroup@smc.vnet.net*Subject*: [mg10703] Re: JordanDecomposition trouble*From*: Paul Abbott <paul@physics.uwa.edu.au>*Date*: Fri, 30 Jan 1998 04:24:38 -0500*Organization*: University of Western Australia*References*: <6ahmmp$pfa@smc.vnet.net>

Josip Loncaric wrote: > Let {s,j} denote Jordan decomposition of the following exact matrix: > > m = {{0,1,0,1},{0,0,0,0},{0,1,0,1},{0,0,0,0}} > {s,j} = JordanDecomposition[m] > > We should have m == s.j.Inverse[s], but in Mathematica 3.01 this is not > the case. > Instead, we get a rather different result: > > In[3]:= s.j.Inverse[s] > Out[3]= {{0,1,0,2},{0,0,0,0},{0,1,0,2},{0,0,0,0}} > > The problem is not in matrix inversion since s.Inverse[s] returns > identity. The source of trouble appears to be in the > JordanDecomposition result. Certainly looks that way. Since Jordan decomposition works with symbolic parameters, looking at In[1]:= m = {{0, 1, 0, 1}, {0, 0, 0, 0}, {0, 1, 0, 1}, {0, 0, 0, a}}; In[2]:= {s, j} = JordanDecomposition[m] In[3]:= s.j.Inverse[s]==m Out[3]= True In[4]:= s Out[4]= 1 1 {{0, 1, 0, -}, {0, 0, 1, 0}, {-1, 1, 0, -}, {0, 0, 0, 1}} a a may give a hint as to why the Jordan decomposition failed. Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul@physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________