# isIrreducible

0th

Percentile

##### Determine reducibility of a matrix

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.

Other PerronFrobeniusDiagnostics: isErgodic, isPrimitive

##### Aliases
• isIrreducible
##### Examples
# NOT RUN {
# 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)

# }

Documentation reproduced from package popdemo, version 1.3-0, License: GPL (>= 2)

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