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# Characteristic Polynomial Calculator

Size of the Matrix:

Matrix

The characteristic polynomial calculator computes the characteristic polynomial of a square matrix 2×2, 3×3, 4×4, or any order matrix.

## Characteristic Polynomial:

The characteristic polynomial of a square matrix is a polynomial containing eigenvalues as roots. The characteristic polynomial equation is derived by equating the polynomial to zero.

“ f(λ) and the formula is given by the f(λ) = det (A – λIn) “

det (A - λI) = 0

Where:

A is a matrix λI is the identity matrix multiplied by “λ”

We need to find the eigenvalues, λ, and A.

Det is the determinant of the matrix If the characteristic polynomial is equated to Zero, then our resulting equation is called the Characteristic polynomial equation, it is also called the determinant equation.

If all the roots of the characteristic equation are, we can say the control system is stable and if all the roots are negative then the control system is considered to be more unstable. The moderation system has positive and negative values, when determined by the characteristic equation calculator.

### How to Find Characteristic Polynomial of a 3× 3 Matrix?

Find the characteristic polynomial of the matrix having 3 rows and 3 columns.

$$\begin{bmatrix}3&5&2 \\ 7&9&3 \\ 4&5&4 \\\end{bmatrix}$$

Solution:

$$\begin{bmatrix}3&5&2 \\ 7&9&3 \\ 4&5&4 \\\end{bmatrix}$$

Subtract the “λ” from the original matric to find the

$$\begin{bmatrix}3-λ&5&2 \\ 7&9-λ&3 \\ 4&5&4-λ\\\end{bmatrix}$$

The characteristic polynomial is the determinant of the obtained matrix. We can solve the 3x3 matrix by the characteristic polynomial of a 3x3 matrix calculator in simple steps.

$$= - λ^{3} + 16 λ^{2} - 17 λ - 19$$

You can use the characteristic polynomial calculator to solve the linear differential characteristic polynomial or characteristic roots. It reduces the steps of solving a long equation as we can find the roots in a matter of moments by the characteristic polynomial equation.

### How Does a Characteristic Polynomial Calculator with Steps Work?

The characteristic polynomial of the matrix calculator requires the following value to find the characteristic polynomial equation.

Input:

• Enter the size of the matrix
• Enter all the coefficient values
• Hit the calculate button

Output:

• The characteristic polynomial equation

### References:

From the source of ocw.mit.edu: Eigenvalues, Characteristic Equation From source of brainly.in : Characteristic Values, control system