givens | R Documentation |
Givens Rotations and QR decomposition
givens(A)
A |
numeric square matrix. |
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)
List with two matrices Q
and R
, Q
orthonormal and
R
upper triangular, such that A=Q%*%R
.
Golub, G. H., and Ch. F. van Loan (1996). Matrix Computations. Third edition, John Hopkins University Press, Baltimore.
householder
## 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))
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