Eigen_pinverse | R Documentation |
Pseudo-inverse of a real or complex matrix (Moore-Penrose generalized inverse).
Eigen_pinverse(M)
M |
a matrix, real or complex, not necessarily square |
The pseudo-inverse matrix of M
.
library(EigenR) M <- rbind( toeplitz(c(3, 2, 1)), toeplitz(c(4, 5, 6)) ) Mplus <- Eigen_pinverse(M) all.equal(M, M %*% Mplus %*% M) all.equal(Mplus, Mplus %*% M %*% Mplus) #' a complex matrix A <- M + 1i * M[, c(3L, 2L, 1L)] Aplus <- Eigen_pinverse(A) AAplus <- A %*% Aplus all.equal(AAplus, t(Conj(AAplus))) #' `A %*% Aplus` is Hermitian AplusA <- Aplus %*% A all.equal(AplusA, t(Conj(AplusA))) #' `Aplus %*% A` is Hermitian
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