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
____________________________________________________________________

```

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