%% Octave session from Lecture 28 on Thursday, Nov 21, 2013 
%%
%% Notice that there might be minor differences between Octave and
%% Matlab, but the results of your calculations should be the same.

octave:2> A = [0 0 .33; .18  0 0 ; 0 .71 .94]
A =
   0.00000   0.00000   0.33000
   0.18000   0.00000   0.00000
   0.00000   0.71000   0.94000

% You can use the inbuilt function eig to find the eigenvalues and the
% corresponding eigenvectors

octave:3> help eig `eig' is a function from
the file /usr/lib/octave/3.6.2/oct/i686-pc-cygwin/eig.oct

 -- Loadable Function: LAMBDA = eig (A)
 -- Loadable Function: LAMBDA = eig (A, B)
 -- Loadable Function: [V, LAMBDA] = eig (A)
 -- Loadable Function: [V, LAMBDA] = eig (A, B)
     Compute the eigenvalues and eigenvectors of a matrix.

     Eigenvalues are computed in a several step process which begins
     with a Hessenberg decomposition, followed by a
     Schur decomposition, from which the eigenvalues are apparent.  The
     eigenvectors, when desired, are computed by further manipulations
     of the Schur decomposition.

     The eigenvalues returned by `eig' are not ordered.

     See also: eigs, svd

Additional help for built-in functions and operators is
available in the on-line version of the manual.  Use the command
`doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help@octave.org
mailing list.

octave:4> [V,L]=eig(A)
V =
   0.68209 + 0.00000i   0.68209 - 0.00000i   0.31754 + 0.00000i
  -0.06241 - 0.58963i  -0.06241 + 0.58963i   0.05811 + 0.00000i
  -0.04505 + 0.42562i  -0.04505 - 0.42562i   0.94646 + 0.00000i
L =
Diagonal Matrix
  -0.02180 + 0.20592i                    0                    0
                    0  -0.02180 - 0.20592i                    0
                    0                    0   0.98359 + 0.00000i

% We could extract the eigenvalues from the diagonal of L using the
% command diag

octave:5> Lambdas = diag(L)
Lambdas =
  -0.02180 + 0.20592i
  -0.02180 - 0.20592i
   0.98359 + 0.00000i

% The absolute values of the eigenvalues are obtained using the
% function abs

octave:6> abs(Lambdas )
ans =
   0.20707
   0.20707
   0.98359