       RE: Re: Possible Bug in Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg90230] RE: [mg90195] Re: Possible Bug in Mathematica 6
• From: "Amir Ahmed Ansari" <aansari at softpak.com>
• Date: Wed, 2 Jul 2008 06:38:09 -0400 (EDT)
• References: <g4d31k\$et0\$1@smc.vnet.net> <200807020928.FAA09861@smc.vnet.net>

```Thanks everyone, especially Jean-Marc Gulliet for all the help. It seems I
actually had the theorem wrong. Instead of using minors (which are many and
can be obtained by deleting many different rows and columns), I was deleting
only the first and last rows and consecutive columns (instead of disparate
columns). Thanks again for the help.

Best,

- Amir

-----Original Message-----
From: Fabian [mailto:NOSPAM_fahasch at yahoo.de]
Sent: Wednesday, July 02, 2008 2:29 PM
To: mathgroup at smc.vnet.net
Subject: [mg90230] [mg90195] Re: Possible Bug in Mathematica 6

On Tue, 1 Jul 2008 11:05:24 +0000 (UTC),
Amir Ahmed Ansari <aansari at softpak.com> wrote:
> Hi,
>
> I tried this on a friend=92s computer using Mathematica 6. Consider the
> following matrix:
>
> {
>     { f_11, f_12, f_13, 0, 0, 0, 0, 0, 0 },
>     { 0, 0, 0, f_21, f_22, f_23, 0, 0, 0 },
>     { 0, 0, 0, 0, 0, 0, ( a f_11 + b f_21 ), ( a f_12 + b f_22 ), =
> ( a f_13 +
> b f_23 ) },
>     { f_21, f_22, f_23, f_11, f_12, f_13, 0, 0, 0 },
>     { ( a f_11 + b f_21 ), ( a f_12 + b f_22 ), ( a f_13 + b f_23 =
> ), 0, 0,
> 0, f_11, f_12, f_13 },
>     { 0, 0, 0, ( a f_11 + b f_21 ), ( a f_12 + b f_22 ), ( a f_13 =
> + b f_23
> ), f_21, f_22, f_23 }
> }
>
>
> All 5x5 have a determinant of 0 as can be seen by using Det[]. Yet,
> MatrixRank[] comes out to be 5. Is this a bug or am I doing something
> stupid?

Hm, do you mean that all 5x5 submatrices have a determinant equal to
0?
Check Minors[matrix,5]

```

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