Here are the results for matrix $C = \begin{bmatrix} 6 & 3 & -8 \\ 0 & -2 & 0 \\ 1 & 0 & -3 \end{bmatrix}$:

1. Characteristic Polynomial Coefficients (PolyCoeffs):
   $1, -1, -16, -20$

2. Eigenvalues (evals):
   $5, -2 + 2.9 \times 10^{-8}i, -2 - 2.9 \times 10^{-8}i$
   The second and third eigenvalues are complex but have a negligible imaginary part, indicating they are approximately $-2$.

3. Eigenvalues from eig() (eigDiag):
   $5, -2, -2$

4. Eigenvectors (eigV) (each column corresponds to an eigenvector):

   0.9923 & 0.7071 & 0.7071 \\ 0 & 0 & 7.327 \times 10^{-16} \\ 0.1240 & 0.7071 & 0.7071 \end{bmatrix}$$

Let me know if you need further details or explanations!

Here are 5 relative questions to consider:

1. How are the eigenvalues of a matrix related to its characteristic polynomial?
2. Why are the eigenvectors normalized to have a magnitude of 1?
3. What is the geometric interpretation of eigenvectors and eigenvalues?
4. How does the multiplicity of eigenvalues affect the matrix's diagonalization?
5. How can you confirm whether a matrix is diagonalizable?

Tip: A matrix is diagonalizable if it has enough linearly independent eigenvectors, equal to its size (n distinct eigenvectors for an $n \times n$ matrix).