# lq: LQ decomposition. In tensr: Covariance Inference and Decompositions for Tensor Datasets

## Description

Computes the LQ decomposition of a matrix.

## Usage

 `1` ```lq(X) ```

## Arguments

 `X` A n by p matrix of rank n.

## Details

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.

## 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.

`qr2` for the related QR decomposition.

## Examples

 ```1 2 3 4 5 6 7 8``` ```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)) ```

### Example output

```           [,1]      [,2]      [,3]
[1,]  1.7013508 0.0000000 0.0000000
[2,] -0.9916113 2.1371754 0.0000000
[3,] -0.1397849 0.5026932 0.8693234
[,1]      [,2]        [,3]
[1,] -0.1505313 0.8094839 -0.07419913
[2,]  0.1372855 0.1322648  0.98136427
[3,]  0.9628331 0.2059868 -0.16394063
[4,] -0.1773286 0.5336772 -0.06739535
[,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1
[,1] [,2] [,3] [,4]
[1,]    0    0    0    0
[2,]    0    0    0    0
[3,]    0    0    0    0
```

tensr documentation built on May 29, 2017, 9:44 a.m.