MATLAB Function Reference |
Syntax
Description
produces the reduced row echelon form of R = rref(A)
A
using Gauss Jordan elimination with partial pivoting. A default tolerance of (max(size(A))*eps *norm(A,inf)
) tests for negligible column elements.
also returns a vector [R,jb] = rref(A)
jb
such that:
r = length(jb)
is this algorithm's idea of the rank of A
.
x(jb)
are the pivot variables in a linear system Ax = b
.
A(:,jb)
is a basis for the range of A
.
R(1:r,jb)
is the r
-by-r
identity matrix.
[R,jb] = rref(A,tol)
uses the given tolerance in the rank tests.
Roundoff errors may cause this algorithm to compute a different value for the rank than rank
, orth
and null
.
Examples
Use rref
on a rank-deficient magic square:
A = magic(4), R = rref(A) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 R = 1 0 0 1 0 1 0 3 0 0 1 -3 0 0 0 0
See Also
round | rsf2csf |
© 1994-2005 The MathWorks, Inc.