# isIrreducible

From popdemo v1.3-0
by Iain Stott

##### 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.

##### See Also

Other PerronFrobeniusDiagnostics: `isErgodic`

,
`isPrimitive`

##### 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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