MoorePenrose | R Documentation |
The Moore-Penrose inverse is a generalization of the regular inverse of a square, non-singular, symmetric matrix to other cases (rectangular, singular), yet retain similar properties to a regular inverse.
MoorePenrose(X, tol = sqrt(.Machine$double.eps))
X |
A numeric matrix |
tol |
Tolerance for a singular (rank-deficient) matrix |
The Moore-Penrose inverse of X
X <- matrix(rnorm(20), ncol=2) # introduce a linear dependency in X[,3] X <- cbind(X, 1.5*X[, 1] - pi*X[, 2]) Y <- MoorePenrose(X) # demonstrate some properties of the M-P inverse # X Y X = X round(X %*% Y %*% X - X, 8) # Y X Y = Y round(Y %*% X %*% Y - Y, 8) # X Y = t(X Y) round(X %*% Y - t(X %*% Y), 8) # Y X = t(Y X) round(Y %*% X - t(Y %*% X), 8)
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