matlib (version 0.6.0)

Inverse: Inverse of a Matrix

Description

Uses gaussianElimination to find the inverse of a square, non-singular matrix, $X$.

Usage

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

Arguments

X

a square numeric matrix

tol

tolerance for checking for 0 pivot

...

other arguments passed on

Value

• the inverse of X

Details

The method is purely didactic: The identity matrix, $I$, is appended to $X$, giving $X | I$. Applying Gaussian elimination gives $I | X^{-1}$, and the portion corresponding to $X^{-1}$ is returned.

Examples

A <- matrix(c(2, 1, -1,
               -3, -1, 2,
               -2,  1, 2), 3, 3, byrow=TRUE)
  Inverse(A)
  Inverse(A, verbose=TRUE, fractions=TRUE)