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 x, |_x_|=int(x) is called the characteristic, where |_x_| 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 u(s)=u(x(s),t(s)). Since


it follows that dt/ds=1, dx/ds=-6u, and du/ds=0. Integrating gives t(s)=s, x(s)=-6su_0(x), and u(s)=u_0(x), where the constants of integration are 0 and u_0(x)=u(x,0).

See also

Character, Character Table, Characteristic Class, Characteristic Equation, Characteristic Factor, Characteristic Function, Characteristic Polynomial, Euler Characteristic, Characterization, Elliptic Characteristic, Field Characteristic, Lyapunov Characteristic Exponent, Lyapunov Characteristic Number, Mantissa, Mathieu Characteristic Exponent, Ordinary Differential Equation, Partial Differential Equation, Plücker Characteristics, Scientific Notation, Segre Characteristic

Explore with Wolfram|Alpha


Farlow, S. J. Partial Differential Equations for Scientists and Engineers. New York: Dover, pp. 205-212, 1993.Landau, L. D. and Lifschitz, E. M. Fluid Mechanics, 2nd ed. Oxford, England: Pergamon Press, pp. 310-346, 1982.Moon, P. and Spencer, D. E. Partial Differential Equations. Lexington, MA: Heath, pp. 27-29, 1969.Whitham, G. B. Linear and Nonlinear Waves. New York: Wiley, pp. 113-142, 1974.Zauderer, E. Partial Differential Equations of Applied Mathematics, 2nd ed. New York: Wiley, pp. 78-121, 1989.Zwillinger, D. "Method of Characteristics." §88 in Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 325-330, 1997.

Referenced on Wolfram|Alpha


Cite this as:

Weisstein, Eric W. "Characteristic." From MathWorld--A Wolfram Web Resource.

Subject classifications