How to check if a matrix has an inverse in the R language

Question

How do you determine if a matrix has an inverse in R?

So is there in R a function that with a matrix input, will return somethin like:

"TRUE" (this matrix has inverse)/"FALSE"(it hasn't ...).

Answer 1

You can try using is.singular.matrix function from matrixcalc package.

To install package:

install.packages("matrixcalc")

To load it:

library(matrixcalc)

To create a matrix:

mymatrix<-matrix(rnorm(4),2,2)

To test it:

is.singular.matrix(mymatrix)

If matrix is invertible it returns FALSE, and if matrix is singlar/non-invertible it returns TRUE.

Answer 2

Using abs(det(M)) > threshold as a way of determining if a matrix is invertible is a very bad idea. Here's an example: consider the class of matrices cI, where I is the identity matrix and c is a constant. If c = 0.01 and I is 10 x 10, then det(cI) = 10^-20, but (cI)^-1 most definitely exists and is simply 100I. If c is small enough, det() will underflow and return 0 even though the matrix is invertible. If you want to use determinants to check invertibility, check instead if the modulus of the log determinant is finite using determinant().