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

*To*: mathgroup at smc.vnet.net*Subject*: [mg126999] Re: multiplying, element wise, a row by each column of a matrix.*From*: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>*Date*: Fri, 22 Jun 2012 05:13:43 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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 Hi, Nasser, The scalar product (Dot[ ]) gives you almost the list like you need. Try this: Clear[v1, v2]; mat = {{a11, a12}, {a21, a22}, {a31, a32}}; v = {v1, v2}; mat.v {a11 v1 + a12 v2, a21 v1 + a22 v2, a31 v1 + a32 v2} Now replace Plus by List: mat.v /. Plus -> List {{a11 v1, a12 v2}, {a21 v1, a22 v2}, {a31 v1, a32 v2}} Have fun, Alexei Alexei BOULBITCH, Dr., habil. IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L-5326 Contern, LUXEMBOURG Office phone : +352-2454-2566 Office fax: +352-2454-3566 mobile phone: +49 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu