MultiStatM (version 2.0.0)

QplicMatr: Qplication Matrix

Description

Restores the duplicated/q-plicated elements which are eliminated by EliminMatr in a T-product of vectors of dimension d.

Usage

QplicMatr(d, q, useSparse = FALSE)

Value

Qplication matrix of order \(d^q \times \eta_{d,q}\), see (1.30), p.15. If useSparse=TRUE an object of the class "dgCMatrix" is produced.

Arguments

d

dimension of a vector x

q

power of the Kronecker product

useSparse

TRUE or FALSE.

Details

Note: since the algorithm of elimination is not unique, q-plication works together with the function EliminMatr only.

References

Gy. Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021, p.21, (1.31)

See Also

Other Matrices and commutators: EliminIndx(), EliminMatr(), QplicIndx(), SymIndx(), SymMatr(), UnivMomCum()

Examples

x<-c(1,2,3)
y<-kronecker(kronecker(x,x),x)
## Distinct elements of y
z<-as.matrix(EliminMatr(3,3))%*%y
## Restore eliminated elements in z
as.vector(QplicMatr(3,3)%*%z)