# Math Help - identity linear operator

1. ## identity linear operator

Let I: V->V be the identity operator on an n-dimensional vector space V defined by I(v)=v for every v in V. Show that the matrix of I with respect to a basis S for V is $I_{n}$.

2. Well it is the identity. So in particular, it takes the first basis element to the first basis element ( $1e_1 + 0e_2 + ... + 0e_n$), the second basis element to the second basis element ( $0e_1 + 1e_2 + ... + 0e_n$), etc.
Thus the first column is [1,0,0...0]
The second Column is [0,1,0,...0]
.
.
.
The nth column is [0,0,...,1]
So $a_{ii}=1$ and $a_{ij}=0$ for $i \not = j$
$a_ij=\delta_{ij}=In$