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

F12147

Formulation 0

Let $A \in \mathbb{C}^{N \times N}$ be a D999: Complex matrix.

Then the following statements are equivalent

(1)	\begin{equation} \text{det}(A) \neq 0 \end{equation}
(2)	\begin{equation} \text{Ker}(A) = \left\{ (0, 0, \ldots, 0)^T \right\} \end{equation}