If $R$ is a division ring, then the direct sum of $n$ copies of $R$ $$ R^n = R \oplus\dotsb\oplus R\text{ (n times),}$$ is a vector space.

The <</SPAN>#46#>standard basis for $R^n$ consists of $n$ elements $$ e_1 = (1,0,\dotsc ,0), \quad e_2 = (0,1,0,\dotsc ,0),\quad \dotsc \quad e_n = (0,\dotsc ,0,1) $$ where each $e_i$ has $1$ for its $i$ component and $0$ for every other component. The $e_i$ are called the standard basis vectors.