What is "characteristic"

Index \In"dex\, n.; pl. E. Indexes, L. Indices(?). [L.: cf. F. index. See Indicate, Diction.]

1. That which points out; that which shows, indicates, manifests, or discloses; as, the increasing unemployment rate is an index of how much the economy has slowed.

   Tastes are the indexes of the different qualities of plants.
   --Arbuthnot.

2. That which guides, points out, informs, or directs; a pointer or a hand that directs to anything, as the hand of a watch, a movable finger or other form of pointer on a gauge, scale, or other graduated instrument. In (printing), a sign [[hand]] (called also fist) used to direct particular attention to a note or paragraph.

3. A table for facilitating reference to topics, names, and the like, in a book, usually giving the page on which a particular word or topic may be found; -- usually alphabetical in arrangement, and printed at the end of the volume. Typically found only in non-fiction books.

4. A prologue indicating what follows. [Obs.]
   --Shak.

5. (Anat.) The second finger, that next to the pollex (thumb), in the manus, or hand; the forefinger; index finger.

6. (Math.) The figure or letter which shows the power or root of a quantity; the exponent. [In this sense the plural is always indices.]

7. The ratio, or formula expressing the ratio, of one dimension of a thing to another dimension; as, the vertical index of the cranium.

8. A number providing a measure of some quantity derived by a formula, usually a form of averaging, from multiple quantities; -- used mostly in economics; as, the index of leading indicators; the index of industrial production; the consumer price index. See, for example, the consumer price index.

9. (computers) A file containing a table with the addresses of data items, arranged for rapid and convenient search for the addresses.

10. (computers) A number which serves as a label for a data item and also represents the address of a data item within a table or array.

11. (R. C. Ch.), The Index prohibitorius, a catalogue of books which are forbidden by the church to be read; also called Index of forbidden books and Index Librorum Prohibitorum.

    Index error, the error in the reading of a mathematical instrument arising from the zero of the index not being in complete adjustment with that of the limb, or with its theoretically perfect position in the instrument; a correction to be applied to the instrument readings equal to the error of the zero adjustment.

    Index expurgatorius. [L.] See Index prohibitorius (below).

    Index finger. See Index, 5.

    Index glass, the mirror on the index of a quadrant, sextant, etc.

    Index hand, the pointer or hand of a clock, watch, or other registering machine; a hand that points to something.

    Index of a logarithm (Math.), the integral part of the logarithm, and always one less than the number of integral figures in the given number. It is also called the characteristic.

    Index of refraction, or Refractive index (Opt.), the number which expresses the ratio of the sine of the angle of incidence to the sine of the angle of refraction. Thus the index of refraction for sulphur is 2, because, when light passes out of air into sulphur, the sine of the angle of incidence is double the sine of the angle of refraction.

    Index plate, a graduated circular plate, or one with circular rows of holes differently spaced; used in machines for graduating circles, cutting gear teeth, etc.

    Index prohibitorius [L.], or Prohibitory index (R. C. Ch.), a catalogue of books which are forbidden by the church to be read; the index expurgatorius [L.], or expurgatory index, is a catalogue of books from which passages marked as against faith or morals must be removed before Catholics can read them. These catalogues are published with additions, from time to time, by the Congregation of the Index, composed of cardinals, theologians, etc., under the sanction of the pope.
    --Hook.

    Index rerum [L.], a tabulated and alphabetized notebook, for systematic preservation of items, quotations, etc.

adjective and noun both first attested 1660s, from character + -istic on model of Greek kharakteristikos. Earlier in the adjectival sense was characteristical (1620s). Related: Characteristically (1640s). Characteristics "distinctive traits" also attested from 1660s.

a. Being a distinguishing feature of a person or thing. n. 1 a distinguishable feature of a person or thing 2 (context mathematics English) the integer part of a logarithm 3 (context nautical English) the distinguishing features of a navigational light on a lighthouse etc by which it can be identified (colour, pattern of flashes etc) 4 (context algebra field theory English) The minimum number of times that the unit of a field must be added unto itself in order to yield that field's zero, or, if that minimum natural number does not exist, then (the integer) zero.

adj. typical or distinctive; "heard my friend's characteristic laugh"; "red and gold are the characteristic colors of autumn"; "stripes characteristic of the zebra" [ant: uncharacteristic]

1. n. a prominent aspect of something; "the map showed roads and other features"; "generosity is one of his best characteristics" [syn: feature]

2. a distinguishing quality

3. the integer part (positive or negative) of the representation of a logarithm; in the expression log 643 = 2.808 the characteristic is 2

4. any measurable property of a device measured under closely specified conditions [syn: device characteristic]

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity element (1) in a sum to get the additive identity element (0); the ring is said to have characteristic zero if this sum never reaches the additive identity.

That is, char(R) is the smallest positive number n such that

$$\underbrace{1+\cdots+1}_{n \text{ summands}} = 0$$

if such a number n exists, and 0 otherwise.

The characteristic may also be taken to be the exponent of the ring's additive group, that is, the smallest positive n such that

$$\underbrace{a+\cdots+a}_{n \text{ summands}} = 0$$

for every element a of the ring (again, if n exists; otherwise zero). Some authors do not include the multiplicative identity element in their requirements for a ring (see ring), and this definition is suitable for that convention; otherwise the two definitions are equivalent due to the distributive law in rings.

Characteristic (from the Greek word for a property, attribute or trait of an entity) may refer to:

In physics and engineering, any characteristic curve that shows the relationship between certain input and output parameters, for example:

• I-V or current-voltage characteristic, the current in a circuit as a function of the applied voltage
• Receiver operating characteristic

In navigation:

• Light characteristic, pattern of a lighted beacon

In mathematics:

• Characteristic (algebra) of a ring, the smallest common cycle length of the ring's addition operation
• Characteristic function (disambiguation), usually the indicator function of a subset, though the term has other meanings in specific domains
• Characteristic polynomial, a polynomial associated to a square matrix in linear algebra
• Characteristic vector (disambiguation), another name for eigenvector of a matrix
• Characteristic value, another name for eigenvalue of a matrix
• Characteristic word, a subclass of Sturmian word
• Euler characteristic, a topological invariant
• Characteristic subgroup, a subgroup that is invariant under all automorphisms in group theory
• Method of characteristics, a technique for solving partial differential equations
• Characteristic, integer part of a common logarithm

In other uses:

• Another name for ability score in Dungeons & Dragons