#' Samples the random variable eta from a matrix normal random variable with appropriate parameters.
#' @param X: X-variable matrix with dimension n cross p.
#' @param U: matrix containing Y variables with dimension n cross r. 
#' @param gamma" matrix with u many orthonormal column. dimension r cross u.  
#' @param C_prior: prior specification. a p cross p variance covariance matrix.
#' @param e_Prior: prior specification. a r cross p matrix. 

SampleEta<-function(X, U, omega, gamma, C_prior=NULL,e_prior=NULL){
  #remember According to the setup C_inv is prior not C check carefully
  # p=dim(X)[2]; r= dim(U)[2]
  if(  is.null(C_prior)  )  {  C_prior=0*diag(dim(X)[2])  }
  if(  is.null(e_prior)  )   {  e_prior=matrix(0,nrow=dim(U)[2],ncol=dim(X)[2]) }
  Sigma2=solve(t(X)%*% X+C_prior)
  e_tilde=(  t(U) %*% X+ e_prior%*% C_prior  ) %*% Sigma2
  Mean=t(gamma)%*% e_tilde # check this 
  Sigma1=diag(omega,nrow=length(omega)); 
  eta=rMatrixNormal(Mean,Sigma1,Sigma2)
  return(eta)
}