Re: Possible Bug in Mathematica 6
- To: mathgroup at smc.vnet.net
- Subject: [mg90241] Re: [mg90184] Possible Bug in Mathematica 6
- From: DrMajorBob <drmajorbob at att.net>
- Date: Thu, 3 Jul 2008 06:11:06 -0400 (EDT)
- References: <19823722.1215015456847.JavaMail.root@m08>
- Reply-to: drmajorbob at longhorns.com
Without the Blanks, results are similar:
m = {{f11, f12, f13, 0, 0, 0, 0, 0, 0}, {0, 0, 0, f21, f22, f23, 0, 0,
0}, {0, 0, 0, 0, 0,
0, (a f11 + b f21), (a f12 + b f22), (a f13 + b f23)}, {f21, f22,
f23, f11, f12, f13, 0, 0,
0}, {(a f11 + b f21), (a f12 + b f22), (a f13 + b f23), 0, 0, 0,
f11, f12, f13}, {0, 0,
0, (a f11 + b f21), (a f12 + b f22), (a f13 + b f23), f21, f22,
f23}};
Dimensions@m
{6, 9}
RowReduce@m
{{1, 0, (f13 f22 - f12 f23)/(-f12 f21 + f11 f22), 0, 0, 0, 0, f12/(
a f11 + b f21), (
f12 (-f13 f21 + f11 f23))/((a f11 + b f21) (-f12 f21 +
f11 f22))}, {0, 1, (f13 f21 - f11 f23)/(f12 f21 - f11 f22), 0, 0,
0, 0, -(f11/(a f11 + b f21)), (
f11 f13 f21 -
f11^2 f23)/((a f11 + b f21) (-f12 f21 + f11 f22))}, {0, 0, 0, 1,
0, (-f13 f22 + f12 f23)/(f12 f21 - f11 f22), 0, f22/(
a f11 + b f21), -((
f22 (f13 f21 - f11 f23))/((a f11 + b f21) (-f12 f21 +
f11 f22)))}, {0, 0, 0, 0, 1, (f13 f21 - f11 f23)/(
f12 f21 - f11 f22),
0, -(f21/(a f11 + b f21)), (-f13 f21^2 +
f11 f21 f23)/((a f11 + b f21) (f12 f21 - f11 f22))}, {0, 0, 0, 0,
0, 0, 1, (a f12 + b f22)/(a f11 + b f21), (a f13 + b f23)/(
a f11 + b f21)}, {0, 0, 0, 0, 0, 0, 0, 0, 0}}
RowReduce@Transpose@m
{{1, 0, 0, 0, 0, a^2/b}, {0, 1, 0, 0, 0, b}, {0, 0, 1, 0, 0, 1/b}, {0,
0, 0, 1, 0, a}, {0, 0, 0, 0, 1, -(a/b)}, {0, 0, 0, 0, 0, 0}, {0, 0,
0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}
MatrixRank@m
5
Bobby
On Wed, 02 Jul 2008 13:43:22 -0500, DrMajorBob <drmajorbob at att.net> wrote:
> I'm curious how you used Det on a 6-by-9 (non-square) matrix:
>
> m = {{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}};
>
> Dimensions@m
>
> {6, 9}
>
> RowReduce@m
>
> {{1, 0, -1, 0, 0, 0, 0, 12/(11 a + 21 b), 24/(11 a + 21 b)}, {0, 1, 2,
> 0, 0, 0, 0, -(11/(11 a + 21 b)), -(22/(11 a + 21 b))}, {0, 0, 0, 1,
> 0, -1, 0, 22/(11 a + 21 b), 44/(11 a + 21 b)}, {0, 0, 0, 0, 1, 2,
> 0, -(21/(11 a + 21 b)), -(42/(11 a + 21 b))}, {0, 0, 0, 0, 0, 0,
> 1, (2 (6 a + 11 b))/(11 a + 21 b), (13 a + 23 b)/(11 a + 21 b)}, {0,
> 0, 0, 0, 0, 0, 0, 0, 0}}
>
> (5 independent rows.)
>
> RowReduce@Transpose@m
>
> {{1, 0, 0, 0, 0, a^2/b}, {0, 1, 0, 0, 0, b}, {0, 0, 1, 0, 0, 1/b}, {0,
> 0, 0, 1, 0, a}, {0, 0, 0, 0, 1, -(a/b)}, {0, 0, 0, 0, 0, 0}, {0, 0,
> 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}
>
> (5 independent columns.)
>
> MatrixRank@m
>
> 5
>
> (Rank 5.)
>
> I don't see a problem.
>
> Bobby
>
> On Tue, 01 Jul 2008 06:02:57 -0500, 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?
>>
>>
>>
>>
>
>
>
--
DrMajorBob at longhorns.com