Eigenvalues of Schur Decomposition

Theorem

Let $\mathbf A$ be a square matrix.

Let $\mathbf A = \mathbf Q \mathbf T \mathbf Q^*$ be a Schur decomposition for $\mathbf A$.

Then the eigenvalues of $\mathbf A$ appear on the main diagonal of $\mathbf T$.

Proof

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Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Schur decomposition (I. Schur, 1909)