Eigenvalues?and?eigenvectors?are properties of square matrices and are used in a lot of real-life applications including geometrical transformations and probability scenarios. In order to find these eigenvalues and eigenvectors, the?characteristic polynomial?for a matrix must be found and solved.

What is a characteristic polynomial?

How do I find the characteristic polynomial?

How do you find the eigenvalues of a matrix?

• For this course, as the characteristic polynomial will always be a?quadratic, the polynomial will always generate one of the following:
  • two real and distinct?eigenvalues,
  • one real repeated?eigenvalue or
  • complex?eigenvalues

How do you find the eigenvectors?of a matrix?