Characteristic polynomial online calculator

Characteristic polynomial of the matrix A, can be calculated by using the formula:

| Aλ E |

где E - identity matrix, which has the same number of rows and columns as initial matrix A

Look closer at the formula above. If matrix A is of the form:


then expression Aλ E has the form:



Finally, we should find the determinant:


After calculating the determinant, we'll get the polynomial of n-th degree (n - order of initial matrix), which depends on variable λ:

P( λ ) = cn λn + cn1 λn1 + ... + ci λi + ... + c1 λ + c0

As soon as to find characteristic polynomial, one need to calculate the determinant, characteristic polynomial can only be found for square matrix.

Our online calculator is able to find characteristic polynomial of the matrix and numbers, fractions and parameters can be entered as elements of the matrix.

Input matrix dimension

Matrix dimension: .

Additional options:

- use Sarrus rule to calculate third order determinants.
A =