Re: Matrix Dot Product

• To: mathgroup at smc.vnet.net
• Subject: [mg52178] Re: [mg52159] Matrix Dot Product
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 14 Nov 2004 04:30:14 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Use Plus@@Flatten[A*B]

dim={2,2};

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

Plus@@Flatten[A*B]

a[1, 1]*b[1, 1] + a[1, 2]*b[1, 2] + a[2, 1]*b[2, 1] +
a[2, 2]*b[2, 2]

dim={2,3,2};

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

Plus@@Flatten[A*B]

a[1, 1, 1]*b[1, 1, 1] + a[1, 1, 2]*b[1, 1, 2] +
a[1, 2, 1]*b[1, 2, 1] + a[1, 2, 2]*b[1, 2, 2] +
a[1, 3, 1]*b[1, 3, 1] + a[1, 3, 2]*b[1, 3, 2] +
a[2, 1, 1]*b[2, 1, 1] + a[2, 1, 2]*b[2, 1, 2] +
a[2, 2, 1]*b[2, 2, 1] + a[2, 2, 2]*b[2, 2, 2] +
a[2, 3, 1]*b[2, 3, 1] + a[2, 3, 2]*b[2, 3, 2]

Bob Hanlon

>
> From: "MacDonald, Calum \(MAT\)" <C.A.MacDonald at gcal.ac.uk>
To: mathgroup at smc.vnet.net
> Date: 2004/11/13 Sat AM 04:40:07 EST
> To: mathgroup at smc.vnet.net
> Subject: [mg52178] [mg52159] Matrix Dot Product
>
> Hi
>
> 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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