lq {tensr} | R Documentation |
LQ decomposition.
Description
Computes the LQ decomposition of a matrix.
Usage
lq(X)
Arguments
X |
A |
Details
If X
is an n
by p
matrix with n \le 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.
Value
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.
Author(s)
David Gerard.
See Also
qr2
for the related QR decomposition.
Examples
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))
[Package tensr version 1.0.1 Index]