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