lq | R Documentation |
Computes the LQ decomposition of a matrix.
lq(X)
X |
A n by p matrix of rank n. |
If X is an n by p matrix with n ≤ p, then
lq
computes the LQ decomposition of X. That is, X
= LQ' where Q is p by n with orthonormal columns
and L is n by n lower triangular with positive
diaognal entries.
L
An n by n lower triangular matrix with
positive diagonal entries.
Q
An n by p matrix with orthonormal columns.
The returned values satisfy X = L %*% t(Q)
, up to
numerical precision.
David Gerard.
qr2
for the related QR decomposition.
X <- matrix(stats::rnorm(12), nrow = 3) lq_X <- lq(X) L <- lq_X$L Q <- lq_X$Q L Q trim(t(Q) %*% Q) trim(X - L%*%t(Q))
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