R: Characteristic Polynomial

charpoly {pracma} | R Documentation

## Characteristic Polynomial

### Description

Computes the characteristic polynomial (and the inverse of the matrix, if requested) using the Faddeew-Leverrier method.

### Usage

    charpoly(a, info = FALSE)

### Arguments

`a` | quadratic matrix; size should not be much larger than 100.
`info` | logical; if true, the inverse matrix will also be reported.

### Details

Computes the characteristic polynomial recursively. In the last step the determinant and the inverse matrix can be determined without any extra cost (if the matrix is not singular).

### Value

Either the characteristic polynomial as numeric vector, or a list with components `cp`, the characteristic polynomial, `det`, the determinant, and `inv`, the inverse matrix, will be returned.

### References

Hou, S.-H. (1998). Classroom Note: A Simple Proof of the Leverrier–Faddeev Characteristic Polynomial Algorithm, SIAM Review, 40(3), pp. 706–709.

### Examples

    a <- magic(5)
    A <- charpoly(a, info = TRUE)
    A$cp
    roots(A$cp)
    A$det
    zapsmall(A$inv %*% a)

[Package pracma version 2.0.4 Index]