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MathGroup Archive 1996

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Re: matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5530] Re: matrix
  • From: "w.meeussen" <w.meeussen at solair4b.eunet.be>
  • Date: Thu, 19 Dec 1996 01:02:30 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

At 19:26 14-12-96 -0500, you wrote:
>Who can help me solve the following problem:
>
>Given two vectors
>v = {1/x^3,x,x,x,1/x,1/x,1/x,x^3}
>w = a{1/x^3,x,x,x,0,0,0,0}
>
>where x is real, find a unitary matrix U which takes v to w:
>U.v == w
>
>(the parameter a normalizes w so it has the same length as v).
>
>The problem here is to find a REALISTIC way to solve this in Mathematica.
>Simply setting this up using Solve etc. crunches away for ever.
>
>Thanks in advance!
>
>Dani
>
>
hi Dani,

sorry if this is stupid, but could it be as simple as: 

u=Table[If[i>4,0,1]If[i==j,1,0],{i,8},{j,8}]

{{1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0,
0}, {0, 0, 0, 1, 0, 0, 0, 0}, 
  {0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0,
0}, {0, 0, 0, 0, 0, 0, 0, 0}}

(a u) . v //InputForm

{a/x^3, a*x, a*x, a*x, 0, 0, 0, 0}

just a Identity matrix with the last 4 diagonal elements set to zero?

Wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen at solair4b.eunet.be



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