tensr (version 1.0.1)

lq: LQ decomposition.

Description

Computes the LQ decomposition of a matrix.

Usage

lq(X)

Arguments

X

A \(n\) by \(p\) matrix of rank \(n\).

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.

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.

See Also

qr2 for the related QR decomposition.

Examples

# NOT RUN {
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))
# }