TensorRank

• To: mathgroup at smc.vnet.net
• Subject: [mg8977] TensorRank
• From: Julian Stoev <stoev at SPAM-RE-MO-VER-usa.net>
• Date: Tue, 7 Oct 1997 03:35:24 -0400
• Organization: Seoul National University, Republic of Korea
• Sender: owner-wri-mathgroup at wolfram.com

```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
--------------------------------------------------------------------------
Julian Stoev <j.h.stoev at ieee.org>       - Ph. D. Student
Intelligent Information Processing Lab. - Seoul National University, Korea
Work: 872-7283, Home: 880-4191          - http://poboxes.com/stoev