ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5568 on D6192: Complex matrix eigenvalue sequence
Subresult of R5567: Eigenvalue sequence for a diagonal complex matrix with constant diagonal
Eigenvalue sequence for an identity complex matrix
Formulation 0
Let $I_N \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that
(i) \begin{equation} I_N = \begin{bmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \vdots & \vdots \\ \vdots & \cdots & \ddots & \vdots \\ 0 & \cdots & \cdots & 1 \end{bmatrix} \end{equation}
Then $1, \, 1, \, \ldots, \, 1$ is a D6192: Complex matrix eigenvalue sequence for $A$.
Proofs
Proof 0
Let $I_N \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that
(i) \begin{equation} I_N = \begin{bmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \vdots & \vdots \\ \vdots & \cdots & \ddots & \vdots \\ 0 & \cdots & \cdots & 1 \end{bmatrix} \end{equation}