% Below is the matrix A.  To load this into Matlab, type the filename in
% the command window-  In this case, DataCh6A
A=[-6 -3 6 1
    -1 2 1 -6
    3 6 3 -2
    6 -3 6 -1
    2 -1 2 3
    -3 6 3 2
    -2 -1 2 -3
    1 2 1 6];

% Normalize each column of A to create the matrix U:
colnorms=sqrt(sum(A.*A));  %This is a row vector corresponding to the column
                           % norms of A
                           
C=repmat(colnorms,8,1);    %Creates a matrix from the row vector by 
                           % duplicating "colnorms" 8 times down, 1 time
                           % across (so it is 8 x 4)
                           
U=A./C;  %Elementwise division