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>
- Gaussian Elimination wont work in my example