# Inverse

From matlib v0.9.2
by Michael Friendly

##### Inverse of a Matrix

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

##### 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.

##### Value

the inverse of `X`

##### Examples

```
# NOT RUN {
A <- matrix(c(2, 1, -1,
-3, -1, 2,
-2, 1, 2), 3, 3, byrow=TRUE)
Inverse(A)
Inverse(A, verbose=TRUE, fractions=TRUE)
# }
```

*Documentation reproduced from package matlib, version 0.9.2, License: GPL (>= 2)*

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