Key points
- Sum of eigenvalues = trace, product = determinant.
- Rank + nullity = number of columns.
- Ax = b is consistent when rank(A) = rank([A | b]); unique solution if that rank = number of unknowns.
- Eigenvalues of a triangular matrix are its diagonal entries.
- If λ is an eigenvalue of A, then λᵏ is one of Aᵏ and 1/λ is one of A⁻¹.
- Real symmetric matrices have real eigenvalues.