%  Octave and Matlab ignore anything that comes after a 
%  percent sign.  Text after percent signs are
%  comments intended for you, the human.
%
% Here are six snippets which you can cut and paste into 
% the online Octave utility.


%%%%%%%%%%%%% SNIPPET 1  %%%%%%%%%%%%%%%%%%%%%
% The following enters a matrix and stores it in the
% variable A
  
A=[1, 2, 3;   %  You could also type all this on one line
  -1, 2, 2;   %  but like this it's easier to see what
  1, 0, 1]    %  you typed
      
% You can now compute the inverse and determinant of A
inv(A)
det(A)

% DIY:
% See what happens if you replace A above with a 
% non invertible matrix like
% A = [1, 1; 2, 2]


%%%%%%%%%%%%% SNIPPET 2  %%%%%%%%%%%%%%%%%%%%%
% Start with our matrix A again
% and multiply it with itself a few times

A=[1, 2, 3;  -1, 2, 2; 1, 0, 1]
B=A*A
A*A*A*A
B*B

% DIY : See what you get when you compute A*inv(A)

%%%%%%%%%%%%% SNIPPET 3  %%%%%%%%%%%%%%%%%%%%%
% Start with our matrix A again
A=[1, 2, 3;  -1, 2, 2; 1, 0, 1]  
% The following command gives you the
% characteristic polynomial of A, i.e.
% det(A - lambda I)

p = poly(A)

% The output is stored in the variable 'p'.  To 
% print this output as a polynomial instead of 
% just the coefficients do this:
polyout(p, "X")

%%%%%%%%%%%%% SNIPPET 4  %%%%%%%%%%%%%%%%%%%%%
% The command 'roots' finds the roots of a polynomial,
% real and complex.
p = [1 3 1 3]
polyout(p, "X")
roots(p)

%%%%%%%%%%%%% SNIPPET 5  %%%%%%%%%%%%%%%%%%%%%
% Start with our matrix A again
A=[1, 2, 3;  -1, 2, 2; 1, 0, 1]  
p = poly(A)
roots(p)
% These are the eigenvlaues of A !

%%%%%%%%%%%%% SNIPPET 6  %%%%%%%%%%%%%%%%%%%%%
% Start with our matrix A again
A=[1, 2, 3;  -1, 2, 2; 1, 0, 1]  
% there's a shortcut to getting the eigenvalues,
% namely
eig(A)
% The following also gives you the eigenvectors
% of A.  The eigenvectors are stored in V and 
% the matrix D is a diagonal matrix with the
% eigenvalues of A on the diagonal.
[V D] = eig(A)