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.
a numeric matrix
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
of the matrix
John Fox and Georges Monette
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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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