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

• To: mathgroup at smc.vnet.net
• Subject: [mg25703] Re: [mg25671] A question of matrix multiply, who can solve it?
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Thu, 19 Oct 2000 04:35:28 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Not so terrible. If you want to multiply matrices you must use "Dot".
"Dot" is the notation for matrix multiplication in Mathematica (The
Book, p.841). For example, try

In[1]:=
Array[A, {3, 3}].Array[B, {3, 3}]

(please notice the dot "." between the two arrays indicating
multiplication), which may be written also as

In[12]:=
Dot[Array[A, {3, 3}], Array[B, {3, 3}]]
Out[12]=
{{A[1, 1] B[1, 1] + A[1, 2] B[2, 1] + A[1, 3] B[3, 1],
A[1, 1] B[1, 2] + A[1, 2] B[2, 2] + A[1, 3] B[3, 2],
A[1, 1] B[1, 3] + A[1, 2] B[2, 3] + A[1, 3] B[3, 3]}, {A[2, 1] B[1,
1] +
A[2, 2] B[2, 1] + A[2, 3] B[3, 1],
A[2, 1] B[1, 2] + A[2, 2] B[2, 2] + A[2, 3] B[3, 2],
A[2, 1] B[1, 3] + A[2, 2] B[2, 3] + A[2, 3] B[3, 3]}, {A[3, 1] B[1,
1] +
A[3, 2] B[2, 1] + A[3, 3] B[3, 1],
A[3, 1] B[1, 2] + A[3, 2] B[2, 2] + A[3, 3] B[3, 2],
A[3, 1] B[1, 3] + A[3, 2] B[2, 3] + A[3, 3] B[3, 3]}}

No mistake.

Tomas Garza
Mexico City

"Chen Jisheng" <chenjs at iopp.ccnu.edu.cn> wrote:

> 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?

```

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