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

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}