% matlabeg.m

%This script shows some basic commands of Matlab.
home
disp('This script shows some of the basic commands of Matlab. Whenever ')
disp('there is a pause, simply hit a key to continue to the next')
disp('command.  You can see this script file by going to File, then')
disp('Open, and then selecting matlabeg.')
disp(' ')
disp('In the following, the command which is used to give')
disp('the result is shown on a line by itself after the explanation.')
disp('  ')
pause
disp('To define a matrix A, you would type')
disp('  ')
disp('A=[1 2 3;4 8 6; 7 2 9]')
disp(' ')
disp('and the output will be')
disp('')
A=[1 2 3;4 8 6; 7 2 9]
disp('')
disp('Note that the columns are separated by spaces (or commas) and the rows')
disp('are separated by semicolons or returns.')
pause
disp('  ')
disp('To change an entry, type')
disp('A(1,1)=-1')
A(1,1)=-1
pause
disp('The transpose of A is obtained by typing ')
disp('A'' ')
A'
disp('Note that when you do not use a variable name, the default')
disp('name is ans.')
pause
disp(' ')
disp('To square a matrix (and give it the name Asq), type')
disp('Asq=A^2')
Asq=A^2
pause
disp('Matlab can also do coordinate-wise calculations. For example,')
disp('to square each entry of a matrix, type')
disp('A.^2')
A.^2
disp('In general, coordinate-wise calculations will use the period along')
disp('the operation.')
disp(' ');
pause
disp('To multiply matrices use *.  For example, type')
disp('B=[5,1,0;4,10 -1;1 2 3]; A*B')
B=[5,1,0;4,10 -1;1 2 3];A*B
disp('Note that since a semicolon was used after the definition of B,')
disp('the matrix B was not shown.  That is, a semicolon will suppress the output.')
pause
disp(' ')

disp('To multiply by the constant 3, type')
disp('3*A')
3*A
pause
disp('  ')
disp('Other arithmetical operations are defined in obvious ways.')
disp('A+B')
disp('A-3*B');
A+B
A-3*B
pause
disp(' ')
disp('To add the constant 2 to all entries, type ')
disp('A+2')
A+2
disp('Better notation for the above would be ')
disp('A+2*ones(3,3)')
A+2*ones(3,3)
pause
disp('To add the constant 2 to the diagonal entries, type')
disp('A+2*eye(3,3)')
A+2*eye(3,3)
pause
disp('The determinant of A is obtained by typing')
disp('det(A)')
det(A)
pause
disp('The rank of A is obtained by typing')
disp('rank(A)')
rank(A)
pause
disp(' ')
disp('The inverse of a matrix (if it exists) can be obtained by typing')
disp('inv(A)')
inv(A)
pause
disp(' ')
disp('The eigenvalues of A are listed in a vector when the following command is typed')
disp('eig(A)')
eig(A)
pause
disp('To see the eigenvalues and eigenvectors, type the following command')
disp('[u,d]= eig(A)')
[u,d]=eig(A)
disp('The d matrix is a diagonal matrix with the eigenvalues on the diagonal. The ')
disp('corresponding columns in the matrix u are eigenvectors.')
disp('If the matrix is diagonalizable, then you should be able to recover A by typing')
disp(' ')
disp('u*d*inv(u)')
u*d*inv(u)
pause
disp('The usual norm of a matrix can by found by typing')
disp('norm(A)')
norm(A)
pause
disp('A basis for the null space of A is given by typing')
disp('null(A)')
null(A)
disp('In this case, A is invertible so its null space is trivial.')
disp('To see a non-trivial example, define')
disp('c=[1 2;2 4]')
c=[1 2;2 4]
disp('and now type')
disp('null(c)')
null(c)
disp('Note that Matlab''s output of vectors is usually given as unit vectors')
disp('and whenever possible, output vectors will be orthogonal.')
pause
disp('  ')
disp('A basis for the range of A is given by typing')
disp('orth(A)')
orth(A)
pause
disp('  ')
disp('To see a basis for the range of the above matrix c, type')
disp('orth(c)')
orth(c)
pause
disp(' ')
disp('To multiply a matrix by a vector, the dimensions must match.  That is, Matlab')
disp('considers vectors as matrices with one row or one column.')
disp(' ')
disp('So first define a vector x. Either use x=[1;1;1] or x=[1 1 1]'' ')
disp('x=[1;1;1]')
x=[1;1;1]
disp('To multiply A times x, type')
disp('b=A*x')
b=A*x
pause
disp('To solve a system of equations (in this case Ax=b for x), type')
disp('A\b')
A\b
pause
disp('  ')
disp('Larger matrices can be defined by using loops. For example')
n=10;
disp('n=10;A=zeros(n,n)')
A=zeros(n,n)
pause
disp('Define a loop to put ones on the super diagonal')
disp('for i=1:n-1;  A(i,i+1)=1; end')
for i=1:n-1
A(i,i+1)=1;
end
A
pause
disp('A=A+A'' ')
A=A+A'
pause
disp('A=A+3*eye(n)')
A=A+3*eye(n)
 pause
 disp('Define corners to be 5.')
 disp('A(n,1)=5')
 disp('A(1,n)=5')
A(n,1)=5;
A(1,n)=5;
A
pause
disp('To get a geometrical picture of A, use the command')
disp('mesh(A)')
mesh(A)
pause
disp(' ')
disp('The same idea is used to graph functions. For example, if you type')
disp('peaks, you will run a built-in script which produces the graph of a surface.')
disp('If you want to see the script, type    type peaks    after this demo finishes.')
disp('peaks')
peaks