> [!summary] The standard basis is the most natural basis for $\mathbb{R}^n$ >[!info]+ Read Time **⏱ 1 min** # Definition The standard basis is the most "natural", default [[Basis|basis]] for any $\mathbb{R}^n$. Which is defined by the [[Sets|set]] $\left\{ \vec{e_{1}}, \vec{e_{2}},\dots,\vec{e_{n}} \right\} \in \mathbb{R}^n$ where each $e_{i}$ is a [[Scalar & Vectors|vector]] with a 1 in the i-th position and 0 in all the other positions. Formally the $e_{i}$ entry is defined as $ \begin{array}{c} \vec{e}_i = \begin{bmatrix} 0 \\ \vdots \\ 1 \quad \text{(at position } i\text{)} \\ \vdots \\ 0 \end{bmatrix} \in \mathbb{R}^n \end{array} $