ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5563 on D6192: Complex matrix eigenvalue sequence
Subresult of R5560: Characteristic polynomial for a triangular complex matrix

Eigenvalue sequence for a triangular complex matrix

Formulation 0

Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that

(i)	$A$ is a D5947: Triangular complex matrix

Then $A_{1, 1}, \, A_{2, 2}, \, \ldots, \, A_{N, N}$ is a D6192: Complex matrix eigenvalue sequence for $A$.

Subresults

▶	R5565: Eigenvalue sequence for a lower triangular complex matrix
▶	R5564: Eigenvalue sequence for an upper triangular complex matrix

Proofs

Proof 0

Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that

(i)	$A$ is a D5947: Triangular complex matrix