# charpoly: Characteristic Polynomial In pracma: Practical Numerical Math Functions

 charpoly 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 Leverrierâ€“Faddeev Characteristic Polynomial Algorithm, SIAM Review, 40(3), pp. 706â€“709.

### Examples

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

pracma documentation built on Nov. 10, 2023, 1:14 a.m.