| matr_Qplication {MultiStatM} | R Documentation |
Qplication Matrix
Description
Restores the duplicated/q-plicated elements which are eliminated by matr_Elimination in a T-product of vectors of dimension d.
Usage
matr_Qplication(d, q, useSparse = FALSE)
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 matr_Elimination only.
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.
References
Gy. Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021, p.21, (1.31)
See Also
Other Matrices and commutators:
indx_Commutator_Kmn(),
indx_Commutator_Kperm(),
indx_Commutator_Mixing(),
indx_Commutator_Moment(),
indx_Elimination(),
indx_Qplication(),
indx_Symmetry(),
indx_UnivMomCum(),
matr_Commutator_Kmn(),
matr_Commutator_Kperm(),
matr_Commutator_Mixing(),
matr_Commutator_Moment(),
matr_Elimination(),
matr_Symmetry()
Examples
x<-c(1,2,3)
y<-kronecker(kronecker(x,x),x)
## Distinct elements of y
z<-as.matrix(matr_Elimination(3,3))%*%y
## Restore eliminated elements in z
as.vector(matr_Qplication(3,3)%*%z)