In linear algebra, functional analysis, and related areas of mathematics, a norm (l-norms) is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).
L1-Norm loss function is known as least absolute deviations (LAD).
It is basically minimizing the sum of the absolute differences 
between the target value 
and the estimated values 
.
L2-Norm loss function is known as least squares error (LSE).
It is basically minimizing the sum of the square of the differences between the target value and the estimated values
Differences between L1-L2 norm
The differences of L1-norm and L2-norm as a loss function are the following.
| L1-norm | L2-norm |
| Robust | Not robust |
| Unstable solution | Stable solution |
| Possible multiple solutions | Only one solution |
