# Ginv

From matlib v0.9.2
by Michael Friendly

##### Generalized Inverse of a Matrix

`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 non-integers as rational numbers

##### 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.

##### Value

the generalized inverse of `A`

, expressed as fractions if `fractions=TRUE`

, or rounded

##### See Also

`ginv`

for a more generally usable function

##### Examples

```
# NOT RUN {
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
# }
```

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

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