Reduced Row Echelon Form
Produces the reduced row echelon form of A using
Gauss Jordan elimination with partial pivoting.
rref(A)
A |
numeric matrix. |
A matrix of “row-reduced echelon form" has the following characteristics:
1. All zero rows are at the bottom of the matrix
2. The leading entry of each nonzero row after the first occurs to the right of the leading entry of the previous row.
3. The leading entry in any nonzero row is 1.
4. All entries in the column above and below a leading 1 are zero.
Roundoff errors may cause this algorithm to compute a different value
for the rank than rank, orth or null.
A matrix the same size as m.
This serves demonstration purposes only; don't use for large matrices.
Weisstein, Eric W. “Echelon Form." From MathWorld – A Wolfram Web Resource.
https://mathworld.wolfram.com/EchelonForm.html
A <- matrix(c(1, 2, 3, 1, 3, 2, 3, 2, 1), 3, 3, byrow = TRUE)
rref(A)
# [,1] [,2] [,3]
# [1,] 1 0 0
# [2,] 0 1 0
# [3,] 0 0 1
A <- matrix(data=c(1, 2, 3, 2, 5, 9, 5, 7, 8,20, 100, 200),
nrow=3, ncol=4, byrow=FALSE)
rref(A)
# 1 0 0 120
# 0 1 0 0
# 0 0 1 -20
# Use rref on a rank-deficient magic square:
A = magic(4)
R = rref(A)
zapsmall(R)
# 1 0 0 1
# 0 1 0 3
# 0 0 1 -3
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