R/hw_5_2_hh.R

In exp500/MAT8054: Provide Solutions of Homework and midterm exam in MAT8054 Class

#' Householder function
#' @export
#' @param x matrix variable


hw5_2_hh <- function(x){
  s2 <- c(crossprod(x, x))
  s <- sign(x[1]) * sqrt(s2)
  d <- 1 / (s2 + s * x[1])
  u <- x
  u[1] <- x[1] + s
  U <- diag(length(x)) - outer(d * u, u)
  list(U = U)
}