       Re: multiplying, element wise, a row by each column of a matrix.

• To: mathgroup at smc.vnet.net
• Subject: [mg126985] Re: multiplying, element wise, a row by each column of a matrix.
• From: Thomas Dowling <thomasgdowling at gmail.com>
• Date: Fri, 22 Jun 2012 02:59:29 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201206210919.FAA16006@smc.vnet.net>

```One possibility:

ReplacePart[#, {1 -> v[] #[], 2 -> v[] #[]}] & /@ mat

Tom Dowling

On Thu, Jun 21, 2012 at 10:19 AM, Nasser M. Abbasi <nma at 12000.org> wrote:

> Any one can think of a better way to do this?
>
> The problem: Given a row vector
>
>    v={v1,v2}
>
> and matrix with same number of columns as v, such as
>
> mat={{a11, a12},
>      {a21, a22},
>      {a31, a32}};
>
> I need to multiply v1 by the first column, then
> multiply v2 by the second column. (i.e. scale each column
> of the matrix by the corresponding "weight" from the
> row).
>
> This results in
>
>  {{a11 v1, a12 v2},
>    {a21 v1, a22 v2},
>   {a31 v1, a32 v2}}
>
> I wanted to find a 'smart' way or good command to do
> it, but so far, had to do it the hard way. I'll show 2
> methods. May be you can find a better functional way
> to solve this:
>
> 1)
> Transpose[MapThread[#1 #2 &, {v, Transpose[mat]}]]
>
> This is not natural solution. need to transposes
> 2 times.
>
> 2)
> KroneckerProduct[{v[[#]]},mat[[All,#]]]&/@ Range[1,Length[v]]
> Transpose[Flatten[%, 1]]
>
> also not too natural. Faltten, transpose, etc... not good.
>
> Fyi, using another system, which starts with the letter
> 'O' and ends with the letters 'VE', I can do the above
> using
>
>       v .* mat
>
> Where the ".*" above means element by element product.
>
> I hope the experts here can find a short/better way to do
> this. I am sure there is, I just can't find it yet, and
> I am not happy with what I came up with so far.
>
> thanks,
> --Nasser
>
>

```

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