RE: column * row ??

• To: mathgroup at smc.vnet.net
• Subject: [mg28812] RE: [mg28791] column * row ??
• From: "David Park" <djmp at earthlink.net>
• Date: Mon, 14 May 2001 01:33:03 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```John,

colvec = {a1, a2, a3};
rowvec = {b1, b2, b3};

Transpose[{colvec}].{rowvec}
{{a1 b1, a1 b2, a1 b3}, {a2 b1, a2 b2, a2 b3}, {a3 b1, a3 b2, a3 b3}}

But probably the more Mathematica way of doing it would be...

Outer[#1 #2 &, colvec, rowvec]
{{a1 b1, a1 b2, a1 b3}, {a2 b1, a2 b2, a2 b3}, {a3 b1, a3 b2, a3 b3}}

David Park

> From: J.R. Chaffer [mailto:jrchaff at mcn.net]
To: mathgroup at smc.vnet.net
>
> Hi there,
>
> Can someone tell me a way to mimic the building of
> an N x N matrix by multiplying a column vector
> on left times a row vector on right ? (both vectors
> of length N) - I mean in Mathematica, of course.
>
> i.e, want the result,
>
> (colvec){a1,a2, .. aN} * (rowvec){b1,b2,..bN} =
>
> result is matrix:
>
> {{a1*b1  a1*b2 .....  a1*bN},
>  {a2*b1  a2*b2 .....  a2*bN},
>   ...     ...          ...  ,
>  {aN*b1  aN*b2 .....  aN*bN}}
>
>
> When I try this in Mathematica all I can figure out
> how to produce is the standard dot-product.  If I
> try the 'transposed' lists/matrices, I get an error,
> even tho the product is defined by basic rules of
> matrix multiplication.
>
> Thanks,
>
> John Chaffer
>

```

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