isIrreducible {popdemo}

Determine reducibility of a matrix

Description

Determine whether a matrix is irreducible or reducible

Usage

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.

See Also

Other PerronFrobeniusDiagnostics: isErgodic(), isPrimitive()

Examples

  # 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)