--- a/scripts/linear-algebra/rank.m	Thu Jul 11 09:30:32 2013 -0700
+++ b/scripts/linear-algebra/rank.m	Thu Jul 11 10:31:32 2013 -0700
@@ -19,7 +19,8 @@
 ## -*- texinfo -*-
 ## @deftypefn  {Function File} {} rank (@var{A})
 ## @deftypefnx {Function File} {} rank (@var{A}, @var{tol})
-## Compute the rank of @var{A}, using the singular value decomposition.
+## Compute the rank of matrix @var{A}, using the singular value decomposition.
+##
 ## The rank is taken to be the number of singular values of @var{A} that
 ## are greater than the specified tolerance @var{tol}.  If the second
 ## argument is omitted, it is taken to be
@@ -31,6 +32,29 @@
 ## @noindent
 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest
 ## singular value of @var{A}.
+##
+## The rank of a matrix is the number of linearly independent rows or
+## columns and determines how many particular solutions exist to a system
+## of equations.  Use @code{null} for finding the remaining homogenous
+## solutions.
+##
+## Example:
+##
+## @example
+## @group
+## x = [1 2 3
+##      4 5 6
+##      7 8 9];
+## rank (x)
+##   @result{} 2
+## @end group
+## @end example
+##
+## @noindent
+## The number of linearly independent rows is only 2 because the final row
+## is a linear combination of -1*row1 + 2*row2.
+##
+## @seealso{null, sprank, svd}
 ## @end deftypefn
 
 ## Author: jwe
@@ -104,6 +128,10 @@
 %! A = eye (100);
 %! assert (rank (A), 100);
 
+%!assert (rank ([]), 0)
+%!assert (rank ([1:9]), 1)
+%!assert (rank ([1:9]'), 1)
+
 %!test
 %! A = [1, 2, 3; 1, 2.001, 3; 1, 2, 3.0000001];
 %! assert (rank (A), 3);