# charpolynom: Characteristic polynomial of a matrix In polyMatrix: Infrastructure for Manipulation Polynomial Matrices

## Description

Characteristic polynomial of a matrix

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```charpolynom(x) ## S4 method for signature 'matrix' charpolynom(x) ## S4 method for signature 'polynomial' charpolynom(x) ## S4 method for signature 'polyMatrix' charpolynom(x) ## S4 method for signature 'polyMatrixCharPolynomial,ANY' x[[i]] ## S4 method for signature 'polyMatrixCharPolynomial' degree(x) ## S4 method for signature 'polyMatrixCharPolynomial' predict(object, newdata) ## S4 method for signature 'polyMatrixCharPolynomial' show(object) ```

## Arguments

 `x` an matrix `i` the degree of the polynomial coefficient to be extract `object` an R object `newdata` the value to be evaluated

## Details

The characteristic polynom of a polynomial matrix is a polynom with polynomial coefficients.

## Value

When the input is a numerical matrix of `matrix` class the value is a `polynomial` object.

When the input is a `polyMatrix` object then the value is `polyMatrixCharClass` class object,

## Methods (by class)

• `matrix`: for numerical matrix it is a polynomial with numerical coefficients

• `polynomial`: for polynomial it treats as a matrix 1x1

• `polyMatrix`: for polynomial matrix has polynomial coefficients

• `x = polyMatrixCharPolynomial,i = ANY`: get polynomial coefficient of characteristic polynomial

• `polyMatrixCharPolynomial`: the degree of char polynomial of polynomial matrix

• `polyMatrixCharPolynomial`: the value of char polynomial in a polynomial point

• `polyMatrixCharPolynomial`: prints out a text representation of a characteristic polynomial of a polynomial matrix

 ```1 2 3 4``` ```# numerical matrices m <- matrix(c(2, 1, -1, 0), 2, 2, byrow=TRUE) charpolynom(m) ```