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Definition D6192
Complex matrix eigenvalue sequence

Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
Let $I_N \in \mathbb{C}^{N \times N}$ be a D5699: Complex identity matrix.
A D5975: Euclidean complex number $(\lambda_1, \ldots, \lambda_N) \in \mathbb{C}^N$ is an eigenvalue sequence for $A$ if and only if $$\forall \, z \in \mathbb{C} : \text{Det}(z I_N - A) = \prod_{n = 1}^N (z - \lambda_n)$$
Results
 ▶ R5531: Eigenvalue sequence exists for every complex square matrix ▶ R5566: Eigenvalue sequence for a diagonal complex matrix ▶ R5567: Eigenvalue sequence for a diagonal complex matrix with constant diagonal ▶ R5565: Eigenvalue sequence for a lower triangular complex matrix ▶ R5563: Eigenvalue sequence for a triangular complex matrix ▶ R5568: Eigenvalue sequence for an identity complex matrix ▶ R5564: Eigenvalue sequence for an upper triangular complex matrix