The identity operator on a vector space 
is the linear operator 
defined by
 |
for every 
.
If 
is a nonzero normed space, then 
is a bounded operator
with operator norm 1.
Identity Operator
See also
Bounded Operator, Identity Function, Identity Map, Linear Operator, Operator NormExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Identity Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IdentityOperator.html