Some miscellaneous commands

An important operator in Matlab is the single quote, which represents the (conjugate) transpose:

>> A = [1 2;3 4] 
A =
     1     2
     3     4
>> A'
ans =
     1     3
     2     4
>> B = A + i*.5*A
B =
   1.0000 + 0.5000i   2.0000 + 1.0000i
   3.0000 + 1.5000i   4.0000 + 2.0000i
>> B'
ans =
   1.0000 - 0.5000i   3.0000 - 1.5000i
   2.0000 - 1.0000i   4.0000 - 2.0000i

In the rare event that the transpose, rather than the conjugate transpose, is needed, the ``.''' operator is used:

>> B.'
ans =
   1.0000 + 0.5000i   3.0000 + 1.5000i
   2.0000 + 1.0000i   4.0000 + 2.0000i

(note that ' and .' are equivalent for matrices with real entries).

The following commands are frequently useful; more information can be obtained from the on-line help system.

Creating matrices

• zeros(m,n) creates an matrix of zeros;
• ones(m,n) creates an matrix of ones;
• eye(n) creates the identity matrix;
• diag(v) (assuming v is an n-vector) creates an diagonal matrix with v on the diagonal.

The commands zeros and ones can be given any number of integer arguments; with k arguments, they each create a k-dimensional array of the indicated size.

formatting display and graphics

• format
  • format short 3.1416
  • format short e 3.1416e+00
  • format long 3.14159265358979
  • format long e 3.141592653589793e+00
  • format compact suppresses extra line feeds (all of the output in this paper is in compact format).
• xlabel('string'), ylabel('string') label the horizontal and vertical axes, respectively, in the current plot;
• title('string') add a title to the current plot;
• axis([a b c d]) change the window on the current graph to ;
• grid adds a rectangular grid to the current plot;
• hold on freezes the current plot so that subsequent graphs will be displayed with the current;
• hold off releases the current plot; the next plot will erase the current before displaying;
• subplot puts multiple plots in one graphics window.

Miscellaneous

• max(x) returns the largest entry of x, if x is a vector; see help max for the result when x is a k-dimensional array;
• min(x) analogous to max;
• abs(x) returns an array of the same size as x whose entries are the magnitudes of the entries of x;
• size(A) returns a vector with the number of rows, columns, etc. of the k-dimensional array A;
• length(x) returns the ``length'' of the array, i.e. max(size(A)).
• save fname saves the current variables to the file named fname.mat;
• load fname load the variables from the file named fname.mat;
• quit exits Matlab