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

| A − λ E |

where E - identity matrix, which has the same number of rows and columns as the 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*, besides the numbers, fractions and parameters can be entered as elements of the matrix.

Characteristic polynomial calculator

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