matlib (version 0.6.0)

Ginv: Generalized Inverse of a Matrix

Description

Ginv returns an arbitrary generalized inverse of the matrix A, using gaussianElimination.

Usage

Ginv(A, tol = sqrt(.Machine$double.eps), verbose = FALSE,
  fractions = FALSE)

Arguments

A

numerical matrix

tol

tolerance for checking for 0 pivot

verbose

logical; if TRUE, print intermediate steps

fractions

logical; if TRUE, try to express nonintegers as rational numbers

Value

• the generalized inverse of A, expressed as fractions if fractions=TRUE, or rounded

Details

A generalized inverse is a matrix $\mathbf{A}^-$ satisfying $\mathbf{A A^- A} = \mathbf{A}$. The purpose of this function is mainly to show how the generalized inverse can be computed using Gaussian elimination.

See Also

ginv for a more generally usable function

Examples

A <- matrix(c(1,2,3,4,5,6,7,8,10), 3, 3) # a nonsingular matrix
A
Ginv(A, fractions=TRUE)  # a generalized inverse of A = inverse of A
round(Ginv(A) %*% A, 6)  # check

B <- matrix(1:9, 3, 3) # a singular matrix
B
Ginv(B, fractions=TRUE)  # a generalized inverse of B
B %*% Ginv(B) %*% B   # check