1. So we find s that make
  2. Then for each eigenvalue, we solve .

  • Finding them isn’t too bad.
  • We start with the definition and then convert it into a homogenous equation:
  • The above equation basically represents x getting squished into the origin, this only happens when the det = 0.
  • Also, by Invertible Matrix Theorem, we know that the non-trivial solutions exist only if the matrix is not invertible.
  • So for non-trivial solutions to exist, , since det is non-zero for invertible matrices.

To solve for this, we define the Characteristic Polynomial of :

  • We find the s that make .
  • This is just a polynomial, so we solve it like normal.