# isIrreducible: Determine reducibility of a matrix In popdemo: Demographic Modelling Using Projection Matrices

## Description

Determine whether a matrix is irreducible or reducible

## Usage

 `1` ```isIrreducible(A) ```

## Arguments

 `A` a square, non-negative numeric matrix of any dimension.

## Details

`isIrreducible` works on the premise that a matrix A is irreducible if and only if (I+A)^(s-1) is positive, where I is the identity matrix of the same dimension as A and s is the dimension of A (Caswell 2001).

## Value

`TRUE` (for an irreducible matrix) or `FALSE` (for a reducible matrix).

## References

• Caswell (2001) matrix Population Models, 2nd. ed. Sinauer.

Other PerronFrobeniusDiagnostics: `isErgodic()`, `isPrimitive()`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ``` # Create a 3x3 irreducible PPM ( A <- matrix(c(0,1,2,0.5,0.1,0,0,0.6,0.6), byrow=TRUE, ncol=3) ) # Diagnose reducibility isIrreducible(A) # Create a 3x3 reducible PPM B<-A; B[3,2] <- 0; B # Diagnose reducibility isIrreducible(B) ```