Notes - Numerical Analysis HT24, Schur decomposition
Only mentioned in the notes as brief aside on the section on computing eigenvalues.
Flashcards
Suppose that $A \in \mathbb C^{n \times n}$. What is the Schur decomposition of $A$, and when does it exist?
\[A = QTQ^\star\]
where $Q$ is a unitary matrix and $T$ is triangular.
It exists for every square matrix.
Suppose that $T$ is a normal matrix. What is special about how it can be diagonalised?
It can be diagonalised by a unitary similarity transformation.