Upper Triangular Matrices

A matrix where $m_{ij}=0$ when $i<j$ For example:

$$\left[\begin{array}{ccc}1& 2& 3\\ 0& 4& 5\\ 0& 0& 6\end{array}\right]$$

Theorems

• Upper Triangular Matrices are Normal If and Only if They are Diagonal
• Characterization of Triangularizability and Diagonalizability in Terms of the Minimal Polynomial