MoorePenrose: Moore-Penrose inverse of a matrix

In friendly/matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

Moore-Penrose inverse of a matrix

Description

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.

Usage

MoorePenrose(X, tol = sqrt(.Machine$double.eps))

Arguments

X	A numeric matrix
tol	Tolerance for a singular (rank-deficient) matrix

Value

The Moore-Penrose inverse of X

Examples

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)

friendly/matlib documentation built on March 3, 2024, 12:18 p.m.