tensr (version 1.0.2)

lq: LQ decomposition.

Description

Computes the LQ decomposition of a matrix.

Usage

lq(X)

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.

Arguments

X

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

Author

David Gerard.

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

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))