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Re: Gaussian Elimination wont work in my example


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


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