The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object,
characteristic class, characteristic
equation, characteristic factor, etc.
However, the unqualified term "characteristic" also has a number of specific
meanings depending on context.
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
it follows that
, and . Integrating gives , , and , where the constants of integration are 0 and .
See also Character
Lyapunov Characteristic Exponent
Lyapunov Characteristic Number
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References Farlow, S. J. New York: Dover, pp. 205-212,
1993. Partial Differential Equations for Scientists and Engineers. Landau, L. D. and Lifschitz, E. M. Oxford, England: Pergamon Press, pp. 310-346, 1982. Fluid
Mechanics, 2nd ed. Moon,
P. and Spencer, D. E. Lexington, MA: Heath, pp. 27-29, 1969. Partial
Differential Equations. Whitham,
G. B. New York: Wiley, pp. 113-142, 1974. Linear
and Nonlinear Waves. Zauderer,
E. New York: Wiley, pp. 78-121,
Differential Equations of Applied Mathematics, 2nd ed. Zwillinger, D. "Method of Characteristics." §88
in Boston, MA: Academic Press, pp. 325-330,
of Differential Equations, 3rd ed. Referenced on Wolfram|Alpha Characteristic
Cite this as:
Weisstein, Eric W. "Characteristic." From
--A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/Characteristic.html