Characteristic

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.

For a real number , is called the characteristic, where is the floor function.

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 .

Wolfram Web Resources