#' 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)
}