matlib (version 0.9.6)

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)

Value

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

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 non-integers as rational numbers, using the fractions function; if you require greater accuracy, you can set the cycles (default 10) and/or max.denominator (default 2000) arguments to fractions as a global option, e.g., options(fractions=list(cycles=100, max.denominator=10^4)).

Author

John Fox

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