function [B] = alignMat(M);

% [B] = alignMat(M);
% Return a 3x3 matrix B that aligns (right multiplying) 
% the first 2 rows of M to the "identity matrix".
% See matrix computations (3rd edition), pp. 601.

F = size(M,1)/2;
C = [M(1,:);M(F+1,:)]'*[1 0 0; 0 1 0];
[u,s,v] = svd(C);
B = u*v';