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Math Calculators ▶ Characteristic Polynomial Calculator

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**Table of Content**

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

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.

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 3×3 matrix by the characteristic polynomial of a 3×3 matrix calculator in simple steps.

$$ = – λ^{3} + 16 λ^{2} – 17 λ – 19 $$

The characteristic polynomial calculator is used 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.

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

From the source of ocw.mit.edu: Eigenvalues, Characteristic Equation

From source of brainly.in : Characteristic Values, control system