function hatA = hat(A,M,N)

% HAT	Matrix in hat format
%	hatA = hat(A,M,N) constructs an (m+n) by (m+n) matrix
%	in which A occupies the first m rows and the first n 
%	columns,in which the remaining columns of the first m 
%	rows contains the m by m unimodular matrix M, in which  
%	the remaining rows of the first n columns contains the
%       n by n unimodular matrix N, and in which the lower right  
%	n by m corner contains only zeros except that the entry 
% 	in the lower left corner is m.
%
%	See also UNHAT, NEWHAT.

%	Adapted from Harold M. Edwards, "Linear Algebra."
%	Written by Serge Tchikanda 02/13/96.

[mA,nA]=size(A);
[mM,nM]=size(M);
[mN,nN]=size(N);

if (mM ~=nM) | (mN ~=mN)
   disp(' ')
   disp('The last two inputs must be square matrices')
end

if (mA ~= mM) 
   disp(' ')
   disp('   The first and second inputs must have the same number of rows')
   break
end

if (nA ~= nN) 
   disp(' ')
   disp('   The first and third inputs must have the same number of columns')
   break
end

if (det(M) ~= 1) | (det(N) ~= 1)
   disp(' ')
   disp('   The last two inputs must be unimodular matrices')
   break
end

hatA = [A M;N zeros(nA,mA)];
[mh,nh]=size(hatA);

hatA(mh,nh)=mA;