pracma (version 1.9.9)

charpoly: 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.

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.

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).

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)