popdemo (version 0.2-3)

is.matrix_irreducible : Determine reducibility of a matrix

Description

Determine whether a matrix is irreducible or reducible

Usage

is.matrix_irreducible(A)

Arguments

A

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

Value

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

Details

is.matrix_irreducible works on the premise that a matrix is irreducible if and only if (I+A) raised to the power of s-1 is positive, where I is the identity matrix of the same dimension as A and s is the dimension of A (see Caswell 2001).

References

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

See Also

is.matrix_primitive, is.matrix_ergodic.

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)
    A

    # Diagnose reducibility
    is.matrix_irreducible(A)

    # Create a 3x3 reducible PPM
    B<-A
    B[3,2] <- 0
    B

    # Diagnose reducibility
    is.matrix_irreducible(B)