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MathGroup Archive 2004

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Re: Matrix Dot Product

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52189] Re: [mg52159] Matrix Dot Product
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sun, 14 Nov 2004 04:30:37 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

You're in luck! Mathematica will do it.

Here are two sample 2 x 2 matrices.

matA = Array[a, {2, 2}]
{{a[1, 1], a[1, 2]}, {a[2, 1], a[2, 2]}}

matB = Array[b, {2, 2}]
{{b[1, 1], b[1, 2]}, {b[2, 1], b[2, 2]}}

Then matrix multiplication is just performed with the 'dot' product.

matA.matB
{{a[1, 1] b[1, 1] + a[1, 2] b[2, 1],
    a[1, 1] b[1, 2] + a[1, 2] b[2, 2]}, {a[2, 1] b[1, 1] + a[2, 2] b[2, 1],
    a[2, 1] b[1, 2] + a[2, 2] b[2, 2]}}

Check out Help/List and Matrices/Matrix Operations for more information and
examples.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

From: MacDonald, Calum (MAT) [mailto:C.A.MacDonald at gcal.ac.uk]
To: mathgroup at smc.vnet.net

Hi

I was wondering if someone could please help me with a command for
calculating the dot product of two (NxN) matrices.

For example, for  two (2x2) matrices, A and B, we define the dot product
as:

A(1,1)*B(1,1) + A(2,1)*B(2,1) + A(1,2)*B(1,2) + A(2,2)*B(2,2)

i.e. we multiply corresponding entries of the matrices and sum these
values.

It is easy to write this in a loop but for large matrices the
calculation is rather slow.

Is there a Mathematica function that I can call that will allow me to do
this faster?

Thanks

Calum







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