##### Example3.2.4

It is worth pointing out that we first encountered a basis long ago when we considered the vectors in $$\real^3\text{:}$$

\begin{equation*} \evec_1 = \threevec{1}{0}{0}, \evec_2 = \threevec{0}{1}{0}, \evec_3 = \threevec{0}{0}{1} \text{.} \end{equation*}

We see that these vectors are, in fact, the columns of the $$3\times3$$ identity matrix, which confirms that this set forms a basis.

More generally, the set of vectors $$\evec_1,\evec_2,\ldots,\evec_m$$ forms a basis for $$\real^m\text{,}$$ which we call the standard basis for $$\real^m\text{.}$$

in-context