This function computes the projection operator $$P_V z= V V^\top z$$

vvtz(v, z)

## Arguments

v orthonormal basis of the space on which z is projected. v is either a matrix or a vector. vector that is projected onto the columns of v

## Value

value of the projection operator

## Details

The above formula is only valid if the columns of v are normalized and mutually orthogonal.

dvvtz

Nicole Kraemer

## 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)