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MathGroup Archive 2000

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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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