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

*To*: mathgroup at smc.vnet.net*Subject*: [mg25725] Re: A question of matrix multiply, who can solve it?*From*: leko at ix.netcom.com (J. Leko)*Date*: Thu, 19 Oct 2000 04:35:55 -0400 (EDT)*References*: <8sjkht$g2h@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <8sjkht$g2h at smc.vnet.net>, Chen Jisheng <chenjs at iopp.ccnu.edu.cn> 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. Actually, Mathematica seems to be performing correctly. In this case, I believe that you asked it to calculate the Outer product of A and B. This is a tensor operation. > Do you think so? How can improve it? If you are looking to multiply two matrices togther as you would in elementary linear algebra (i.e., row x column), then what you want to perform is an Inner or Dot product. Try the following example: In[17]:= a = Array[x, {2, 2}] b = Array[y, {2, 2}] a . b Out[17]= {{x[1, 1], x[1, 2]}, {x[2, 1], x[2, 2]}} Out[18]= {{y[1, 1], y[1, 2]}, {y[2, 1], y[2, 2]}} Out[19]= {{x[1, 1] y[1, 1] + x[1, 2] y[2, 1], x[1, 1] y[1, 2] + x[1, 2] y[2, 2]}, {x[2, 1] y[1, 1] + x[2, 2] y[2, 1], x[2, 1] y[1, 2] + x[2, 2] y[2, 2]}} I am sorry that I cannot properly format these expressions in the newsreader. You can have Mathematica properly format the a.b expression by appending //MatrixForm to its end, like this: a . b//MatrixForm This should be more of what you are accustomed to seeing. Regards, J. Leko Please e-mail replies to leko*j at cspar.uah.edu and remove the *