Re: TensorRank

• To: mathgroup at smc.vnet.net
• Subject: [mg9033] Re: [mg8977] TensorRank
• From: seanross at worldnet.att.net
• Date: Wed, 8 Oct 1997 00:05:30 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Julian Stoev wrote:
>
> Dear Group,
> I am not 100% sure, but I am using TensorRank as a function to determine a
> rank of a matrix.
> The  folowing result is surprising for me.
> The determinant<>0, but rank is defficient.
> Am I wrong to use TensorRank in this way?
> Thank you!
>
> In[1]:=
> 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}}
> TensorRank[cm]
> Det[cm]
> Out[1]=
>            1            1            k        k         k       k
> {{0, 0, 0, -}, {0, 0, -(-), 0}, {0, ---, 0, -(--)}, {-(---), 0, --, 0}}
>            j            j           i j        2       i j       2
>                                               j                 j
> Out[2]=
> 2
> Out[3]=
>   2
>  k
> -----
>  2  4
> i  j
> ------------------------------------------------------------------------
I don't understand the problem you are having.  cm is a 4x4 matrix so it
is a second rank tensor, which is exactly what TensorRank[cm] returns.
What would you like TensorRank to return?  Perhaps you want the
dimensions of cm instead?  Dimensions[cm] returns {4,4}

```

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