Projectin operator

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.
z	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.

See also

dvvtz

Author

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)