RANK Calculate the Rank of a Matrix

Section: Array Generation and Manipulations

Usage

Returns the rank of a matrix. There are two ways to use the rank function is 
   y = rank(A,tol)

where tol is the tolerance to use when computing the rank. The second form is 

   y = rank(A)

in which case the tolerance tol is chosen as 

   tol = max(size(A))*max(s)*eps,

where s is the vector of singular values of A. The rank is computed using the singular value decomposition svd.

Examples

Some examples of matrix rank calculations 
--> rank([1,3,2;4,5,6])

ans = 
 2 

--> rank([1,2,3;2,4,6])

ans = 
 1

Here we construct an ill-conditioned matrix, and show the use of the tol argument. 

--> A = [1,0;0,eps/2]

A = 
    1.0000         0 
         0    0.0000 

--> rank(A)

ans = 
 1 

--> rank(A,eps/8)

ans = 
 2