The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object,
for example characteristic class, characteristic
equation, characteristic factor, etc.
However, the unqualified term "characteristic" also has a number of specific
meanings depending on context.
A path in a two-dimensional plane used to transform partial differential equations into systems of ordinary
differential equations is also called a characteristic. This form of characteristic
was invented by Riemann. For an example of the use of characteristics, consider the
equation
Now let .
Since
it follows that ,
, and . Integrating gives , , and , where the constants of integration are 0 and .
, 
is called the characteristic, where 
is the floor function.
.
Since
,
, and 
. Integrating gives 
, 
, and 
, where the constants of integration are 0 and 
.
