ThmDex – An index of mathematical definitions, results, and conjectures.
F13004
Formulation 0
Let $I_N \in \mathbb{R}^{N \times N}$ be a D5621: Real identity matrix such that
(i) $e_1, \ldots, e_N \in \mathbb{R}^{N \times 1}$ are each a D5200: Real column matrix
(ii) \begin{equation} I_N = \begin{bmatrix} e_1 & e_2 & \cdots & e_N \end{bmatrix} \end{equation}
Then \begin{equation} \text{Span} \langle e_1, \ldots, e_N \rangle = \mathbb{R}^{N \times 1} \end{equation}