# Characteristic polynomial online calculator

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

| A − λ 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 A − λ 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 )
=
c_{n} λ ^{n}
+
c_{n−1} λ ^{n−1}
+ ... +
c_{i} λ ^{i}
+ ... +
c_{1} λ
+
c_{0}

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:

A = |