Documentation

rref

Reduced row echelon form (Gauss-Jordan elimination)

Syntax

R = rref(A)
[R,jb] = rref(A)
[R,jb] = rref(A,tol)

Description

R = rref(A)produces the reduced row echelon form ofAusing Gauss Jordan elimination with partial pivoting. A default tolerance of (max(size(A))*eps *norm(A,inf)) tests for negligible column elements.

[R,jb] = rref(A)also returns a vectorjbsuch that:

  • r = length(jb)is this algorithm's idea of the rank ofA.

  • x(jb)are the pivot variables in a linear systemAx = b.

  • A(:,jb)is a basis for the range ofA.

  • R(1:r,jb)is ther-by-ridentity 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 thanrank,orthandnull. Additionally, usemldivideto solve linear systems when high precision is required.

Examples

Userrefon 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

||

Introduced before R2006a

Was this topic helpful?
MATLAB Documentation
Other Documentation
金宝app

Try MATLAB, Simulink, and Other Products

Get trial now