Re: Gaussian Elimination wont work in my example

*To*: mathgroup at smc.vnet.net*Subject*: [mg13450] Re: [mg13429] Gaussian Elimination wont work in my example*From*: Daniel Lichtblau <danl>*Date*: Fri, 24 Jul 1998 01:45:37 -0400*References*: <199807230733.DAA05579@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Cheng L L wrote: > > I have tried to solve a matrix > > {{-4, -2},{-2, -1}]. e =0 where e is a 1x2 matrix say [{a, b}] and > Tranpose[Conjugate[e]].e =1. I use Guassian Elimanation "LinearSolve" > to solve this equation, but it all the time gives out {0,0}, the answer > is not what I want in my case. Please help me to solve this puzzle. > Many thanks. > > Best regards, > LL Cheng > (City University of Hong Kong, EE Dept) > > email : eeacheng at cityu.edu.hk LinearSolve will only give a particular solution, and in the homogeneous case that will be a vector of zeroes. Not what you wanted. To get a basis for all solutions you might use NullSpace as below. In[1]:= mat = {{-4, -2},{-2, -1}}; In[2]:= NullSpace[mat] Out[2]= {{-1, 2}} In[3]:= e = %[[1]]; In[4]:= norm[vec_] := Sqrt[Conjugate[vec].vec] In[5]:= e/norm[e] 1 2 Out[5]= {-(-------), -------} Sqrt[5] Sqrt[5] Daniel Lichtblau Wolfram Research

**References**:**Gaussian Elimination wont work in my example***From:*Cheng L L <eeacheng@cityu.edu.hk>