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lower diagonal matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg80391] lower diagonal matrix
• From: Sean Bonness <nbonness at chem.ucsb.edu>
• Date: Tue, 21 Aug 2007 05:01:06 -0400 (EDT)

Hello...

I am in need of some help in trying to convert data I got from  
another program into mathematica so that I can eventually diagonalize  
the matrix. What I have from the other program are values for a lower  
diagonal matrix, which corresponds to a full symmetric matrix and  
whereby the program tries to save on writing alot of data by just  
writing the lower diagonal matrix. The values I have from another  
program are in a five column by 56 row matrix. The first element  
(1,1) in this matrix corresponds to the (1,1) element in a lower  
diagonal matrix, the second element (1,2) corresponds to (2,1), the  
third (1,3) corresponds to (2,2), the fourth (1,4) corresponds to  
(3,1), the fifth (1,5) corresponds to (3,2), the sixth (2,1)  
corresponds to (3,3) and so on. What I have done so far is read in  
the data into mathematica, but when I do it reads it in as a one  
dimensional list. What I would like to do is to break up the data  
into a human readable form of a lower diagonal matrix and then  
construct a full symmetric (23x23) matrix of this data so as to  
eventually diagonalize and solve it. The lower diagonal elements are  
the same as the upper diagonal elements, so I understand that I would  
need to specify the elements to be a[i,j]=a[j,i] somewhere in  
defining the symmetric matrix. Any help in trying to help me write/ 
construct the full symmetric matrix from the data I have would be  
much appreciated.