[LinearAlgebra] Re: Matrix Dot Product

• To: mathgroup at smc.vnet.net
• Subject: [mg52227] [LinearAlgebra] Re: Matrix Dot Product
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 15 Nov 2004 03:17:37 -0500 (EST)
• Organization: The University of Western Australia
• References: <cn4lbm\$13s\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <cn4lbm\$13s\$1 at smc.vnet.net>,
"MacDonald, Calum \(MAT\)" <C.A.MacDonald at gcal.ac.uk> wrote:

> 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.

This is, of course, not Mathematica's Dot product.

> 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?

As others have pointed out, you can use Dot after applying Flatten to
each matrix. A faster solution is to use direct "element by element"
multiplication and then apply Total. For example, the following code
(borrowed from Bob Hanlon) works in any number of dimensions:

dim={2,3};

A=Array[a,dim];
B=Array[b,dim];

Total[A B, Length[dim]]

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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