The special properties of eigenvalues

Now that we have gone through the concept of the trace and determinant, let's quickly look at some cool properties they have in relation to eigenvalues.

It happens that the sum of the eigenvalues of a matrix equals the trace of the matrix:

Additionally, the product of all the eigenvalues of a matrix is equal to the determinant:

I encourage you to go back to the matrices we have used as examples with their eigenvalues and prove to yourself that this is indeed true!