QR | R Documentation |
QR
computes the QR decomposition of a matrix, X, that is an orthonormal matrix, Q and an upper triangular
matrix, R, such that X = Q R.
QR(X, tol = sqrt(.Machine$double.eps))
X |
a numeric matrix |
tol |
tolerance for detecting linear dependencies in the columns of |
The QR decomposition plays an important role in many statistical techniques.
In particular it can be used to solve the equation Ax = b for given matrix A and vector b.
The function is included here simply to show the algorithm of Gram-Schmidt orthogonalization. The standard
qr
function is faster and more accurate.
a list of three elements, consisting of an orthonormal matrix Q
, an upper triangular matrix R
, and the rank
of the matrix X
John Fox and Georges Monette
qr
A <- matrix(c(1,2,3,4,5,6,7,8,10), 3, 3) # a square nonsingular matrix res <- QR(A) res q <- res$Q zapsmall( t(q) %*% q) # check that q' q = I r <- res$R q %*% r # check that q r = A # relation to determinant: det(A) = prod(diag(R)) det(A) prod(diag(r)) B <- matrix(1:9, 3, 3) # a singular matrix QR(B)
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