R: Givens Rotation

givens {pracma} | R Documentation

## Givens Rotation

### Description

Givens Rotations and QR decomposition

### Usage

    givens(A)

### Arguments

`A` | numeric square matrix.

### Details

`givens(A)` returns a QR decomposition (or factorization) of the square matrix `A` by applying unitary 2-by-2 matrices `U` such that `U * [xk;xl] = [x,0]` where `x=sqrt(xk^2+xl^2)`

### Value

List with two matrices `Q` and `R`, `Q` orthonormal and `R` upper triangular, such that `A=Q%*%R`.

### References

Golub, G. H., and Ch. F. van Loan (1996). Matrix Computations. Third edition, John Hopkins University Press, Baltimore.

### See Also

`householder`

### Examples

    ##  QR decomposition
    A <- matrix(c(0,-4,2, 6,-3,-2, 8,1,-1), 3, 3, byrow=TRUE)
    gv <- givens(A)
    (Q <- gv$Q); (R <- gv$R)
    zapsmall(Q %*% R)

    givens(magic(5))

[Package pracma version 2.0.4 Index]