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}