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#' Projectin operator
#'
#' This function computes the projection operator \deqn{P_V z= V V^\top z}
#'
#' The above formula is only valid if the columns of \code{v} are normalized
#' and mutually orthogonal.
#'
#' @param v orthonormal basis of the space on which \code{z} is projected.
#' \code{v} is either a matrix or a vector.
#' @param z vector that is projected onto the columns of \code{v}
#' @return value of the projection operator
#' @author Nicole Kraemer
#' @seealso \code{\link{dvvtz}}
#' @keywords math
#' @examples
#'
#' # generate random orthogonal vectors
#' X<-matrix(rnorm(10*100),ncol=10) # random data
#' S<-cor(X) # correlation matrix of data
#' v<-eigen(S)$vectors[,1:3] # first three eigenvectors of correlation matrix
#' z<-rnorm(10) # random vector z
#' projection.z<-vvtz(v,z)
#'
#'
#' @export vvtz
vvtz <-
function(v,z){
dummy<-v%*%(t(v)%*%z)
dummy<-as.vector(dummy)
return(dummy)
}
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