# MoorePenrose

From matlib v0.9.2
by Michael Friendly

##### Moore-Penrose inverse of a matrix

The Moore-Penrose inverse is a generalization of the regular inverse of a square, non-singular, symmetric matrix to other cases (rectangular, singular), yet retain similar properties to a regular inverse.

##### Usage

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

##### Arguments

- X
A numeric matrix

- tol
Tolerance for a singular (rank-deficient) matrix

##### Value

The Moore-Penrose inverse of `X`

##### Examples

```
# NOT RUN {
X <- matrix(rnorm(20), ncol=2)
# introduce a linear dependency in X[,3]
X <- cbind(X, 1.5*X[, 1] - pi*X[, 2])
Y <- MoorePenrose(X)
# demonstrate some properties of the M-P inverse
# X Y X = X
round(X %*% Y %*% X - X, 8)
# Y X Y = Y
round(Y %*% X %*% Y - Y, 8)
# X Y = t(X Y)
round(X %*% Y - t(X %*% Y), 8)
# Y X = t(Y X)
round(Y %*% X - t(Y %*% X), 8)
# }
```

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

### Community examples

Looks like there are no examples yet.