| 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)