></div></div></div></div>
<!-- 
##### SOURCE BEGIN #####
%% 
% We illustrate a few steps of the Arnoldi iteration for a small matrix.

A = magic(6);
%% 
% The seed vector determines the first member of the orthonormal basis.
%%
u = randn(6,1);
Q = u/norm(u);
%% 
% Multiplication by $\mathbf{A}$ gives us a new vector in $\mathcal{K}_2$. 
%%
Aq = A*Q(:,1);
%% 
% We subtract off its projection in the previous direction. The remainder 
% is rescaled to give us the next orthonormal column.
%%
v = Aq - (Q(:,1)'*A