Re: TensorRank

*To*: mathgroup at smc.vnet.net*Subject*: [mg9009] Re: TensorRank*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Wed, 8 Oct 1997 00:05:07 -0400*Organization*: University of Western Australia*Sender*: owner-wri-mathgroup at wolfram.com

Julian Stoev wrote: > I am not 100% sure, but I am using TensorRank as a function to determine a > rank of a matrix. > Am I wrong to use TensorRank in this way? Yes. In[1]:= ?TensorRank "TensorRank[expr] gives the depth to which expr is a full array, with all the parts at a particular level being lists of the same length." so TensorRank is only looking at the structure of the tensor. > In[2]:= cm={{0, 0, 0, 1/j}, {0, 0, -(1/j), 0}, {0, k/(i*j), 0, -(k/j^2)}, > {-(k/(i*j)), 0, > k/j^2, 0}} > > The determinant<>0, but rank is defficient. One solution is to look at the NullSpace: In[3]:= ?NullSpace "NullSpace[m] gives a list of vectors that forms a basis for the null space of the matrix m." In[4]:= NullSpace[cm] Out[4]= {} See 3.7.8 Solving Linear Systems in the Mathematica book. 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 at physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________