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 .