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?