echo off
disp('MINIMAT will evaluate complicated expressions describing matrix')
disp('calculations.  It will make up a random matrix of any size:')
echo on
A = rand(3,5)
echo off
pause
disp(' or a matrix with a specified diagonal: ')
echo on
D = diag([1,2,3,4])
echo off
pause
disp('It can calculate the inverse of a matrix: ')
echo on
A = D+rand(4,4)
B=inv(A)
echo off
pause
disp('and multiply matrices (B really is A^(-1)  ): ')
echo on
A*B
echo off
pause
disp('The following illustrates the use of the .m file  gj.m  ')
disp('It computes the Reduced Row Echelon form. ')
echo on
A=[1 2 3; 4 5 6; 7 8 9]
R=gj(A)
pause
echo off
disp('The matrix  A  has rank 2 so the equations   A*X=0   have')
disp('a non trivial solution. Using  R  we can find one. ')
pause
echo on
X=[R(1,3) R(2,3)  -1]
R*X'
A*X'
pause
echo off
disp('The following illustrates the computation of eigenvalues.')
disp('The matrix D is a diagonal matrix with the eigenvalues of')
disp('of  A  on the diagonal, and  V  is a matrix with the')
disp('corresponding eigenvectors of  A as columns.')
echo on
A = rand(3,3)
pause
[V D] = eig(A)
echo off
pause
disp('Note that A*V=V*D:')
echo on
A*V
V*D
echo off
pause
disp('Now we illustrate the singular value decomposition:')
echo on
A=rand(3,4)
pause
[U D V]=svd(A)
echo off
pause
disp('note that  U  and  V  are orthogonal matrices:')
echo on
U*U'
V*V'
echo off
pause
disp('and that the diagonal matrix  D  represents  A in the new bases:')
echo on
U*D*V'
A
echo off
pause
disp('You can use the cursor keys (press [F2] for help) to examine output')
disp('that has scrolled off the screen. The prompt line at the top of the')
disp('screen tells you what function keys to use to invoke menus and get')
disp('help. Use the command     type  mmdemo.m     to view this batch file')
disp('or enter some minimat expressions and/or commands at the #> prompt')
disp('Try it yourself!')