How to check if something is an eigenvalue of a matrix?

If the square matrix is [A], then any eigenvalue, λ, satisfied the equation
[A] = λ[I]
where [I] is the identity matrix of the same size as [A].

To test whether λ is an eigenvalue, verify that
det([A] - λ[I]) = 0

Example:
Test whether 25.06 is an eigenvalue of the following matrix:

Test the determinant of [A] - 25.06[I] to see whether it is zero.


This determinant is not zero, but it is small compared with the diagonal elements of [A].
In practical terms (such as in engineering or physics) it is close to an eigenvalue of [A].
The actual eigenvalue is 25.0626

Hope i can you!