how to solve a linear system of eqs.

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#1290

From: jtrsmith
Date: Fri, 30 Sep 1994 16:22

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I have a system of linear eqs and find it difficult to get a solution:

     (Diag(a)*E -Diag(Ea)) X = b
     trace(X) = 0 

  where a and b are n-dimensional vectors, E is a NxN symmetric matrix.
a, b, E are given.

(Note: only N eqs. of the above are linear independent. It's know that
 trace(b) = 0 which makes sure that the system has a unique solution)

Could anyone help me to solve it? Thanks.

George Cheng.
(If possible, please respond to my account)
-----------------------------------
if N=2, then the solution is:
     X =-D  b
      1   12 1
 
     X =-D  b
      2   21 2

  where D  = 1/E
         ij     ij
-----------------------------------
(   trace(X) here means the sum of all elements of vector X,
    Diag(X) means a diagonal matrix with the elements of X as the
diagonal elements of the matrix)

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From: jtrsmith@garnet.berkeley.edu ()
Newsgroups: sci.math.num-analysis,sci.math,sci.math.symbolic,ucb.math,fj.sci.math,ucb.math.seminars
Subject: how to solve a linear system of eqs.
Date: 30 Sep 1994 16:22:02 GMT
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