Re: A question of matrix multiply, who can solve it?

• To: mathgroup at smc.vnet.net
• Subject: [mg25677] Re: A question of matrix multiply, who can solve it?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 19 Oct 2000 04:35:09 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <8sjkht\$g2h@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hmm,

More strange things happends Dot[A,B] are not the same as
Outer[Times,A,B} and
different form A*B. So what can we do in this situation ? First of all
we should look what "multiply" with tensors mean.

It *is* terrible that tensors can multiplyed in three different ways.

If you wish to calculate the inner product you should use A.B
If you wish a element wise multiply Times[] or A*B is needed.
If you wish to calculate the outer product Outer[] may help.

Since it is not clear what kind of multiplication you want, no one
can say if you output is correct.

Regards
Jens

Chen Jisheng wrote:
>
> Dear Sir,
>
> As a beginning user, I find a mistake of Mathematic 4.0(/3.0 for student).
>
> That is about the multipy method of matrix.
>
> For example, as I input the two matrices:
>
> A={a[1, 1], a[1, 2], a[1, 3], a[1, 4], a[1, 5]}
> {a[2, 1], a[2, 2], a[2, 3], a[2, 4], a[2, 5]}
> {a[3, 1], a[3, 2], a[3, 3], a[3, 4], a[3, 5]}
> {a[4, 1], a[4, 2], a[4, 3], a[4, 4], a[4, 5]}
> {a[5, 1], a[5, 2], a[5, 3], a[5, 4], a[5, 5]},
> B={{b[1, 1], b[1, 2], b[1, 3], b[1, 4], b[1, 5]},
>
>  {b[2, 1], b[2, 2], b[2, 3], b[2, 4], b[2, 5]},
>
>  {b[3, 1], b[3, 2], b[3, 3], b[3, 4], b[3, 5]},
>
>  {b[4, 1], b[4, 2], b[4, 3], b[4, 4], b[4, 5]},
>
>  {b[5, 1], b[5, 2], b[5, 3], b[5, 4], b[5, 5]}},
>
> then calculate the result of A B. The mathematics gives the following
> result:
>
> A B={{a[1, 1] b[1, 1], a[1, 2] b[1, 2], a[1, 3] b[1, 3],
>
>   a[1, 4] b[1, 4], a[1, 5] b[1, 5]},
>
>  {a[2, 1] b[2, 1], a[2, 2] b[2, 2], a[2, 3] b[2, 3],
>
>   a[2, 4] b[2, 4], a[2, 5] b[2, 5]},
>
>  {a[3, 1] b[3, 1], a[3, 2] b[3, 2], a[3, 3] b[3, 3],
>
>   a[3, 4] b[3, 4], a[3, 5] b[3, 5]},
>
>  {a[4, 1] b[4, 1], a[4, 2] b[4, 2], a[4, 3] b[4, 3],
>
>   a[4, 4] b[4, 4], a[4, 5] b[4, 5]},
>
>  {a[5, 1] b[5, 1], a[5, 2] b[5, 2], a[5, 3] b[5, 3],
>
>   a[5, 4] b[5, 4], a[5, 5] b[5, 5]}}.
>
> As all knows, this is not correct. I think it is terrible.
>
> Do you think so? How can improve it?
>
> Looking forward to receiving the reply.
>
> J.-S CHen,
> Institute of Particle Physics,
> Hua-Zhong Normal University,
> Wuhan 430079,China

```

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