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rref, rrefmovie | Examples See Also |
R = rref(A) [R,jb] = rref(A) [R,jb] = rref(A,tol) rrefmovie(A)
R = rref(A)
produces the reduced row echelon form of A
using 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 vector jb
so that:
r = length(jb)
is this algorithm's idea of the rank of A
,
x(jb)
are the bound 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
.
rrefmovie(A)
shows a movie of the algorithm working.
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
inv
Matrix inverse
lu
LU matrix factorization
rank
Rank of a matrix