absolute value

Math.1. the magnitude of a quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as 3 or 3 is 3.2. the square root of the sum of the squares of the real and imaginary parts of a given complex number, as a + bi is equal to the square root of a^{2}+b^{2}. Also called modulus.[190510]
* * *
Geometrically, the absolute value represents (absolute) displacement from the origin (or zero) and is therefore always nonnegative. If a real number a is positive or zero, its absolute value is itself; if a is negative, its absolute value is a. A complex number z is typically represented by an ordered pair (a, b) in the complex plane. Thus, the absolute value (or modulus) of z is defined as the real number a^{2} + b^{2}, which corresponds to z's distance from the origin of the complex plane. Vectors, like arrows, have both magnitude and direction, and their algebraic representation follows from placing their "tail" at the origin of a multidimensional space and extracting the corresponding coordinates, or components, of their "point." The absolute value (magnitude) of a vector is then given by the square root of the sum of the squares of its components. For example, a threedimensional vector v, given by (a, b, c), has absolute value a^{2}/n+/nb^{2}/n+/nc^{2}. Absolute value is symbolized by vertical bars, as in x, z, or v, and obeys certain fundamental properties, such as a · b = a · b and a + b ≤ a + b.* * *
Measure of the magnitude of a real number, complex number, or vector. Geometrically, the absolute value represents (absolute) displacement from the origin (or zero) and is therefore always nonnegative. If a real number a is positive or zero, its absolute value is itself; if a is negative, its absolute value is −a. A complex number z is typically represented by an ordered pair (a, b) in the complex plane. Thus, the absolute value (or modulus) of z is defined as the real number √(a^{2} + b^{2}) , which corresponds to z's distance from the origin of the complex plane. Vectors, like arrows, have both magnitude and direction, and their algebraic representation follows from placing their “tail” at the origin of a multidimensional space and extracting the corresponding coordinates, or components, of their “point.” The absolute value (magnitude) of a vector is then given by the square root of the sum of the squares of its components. For example, a threedimensional vector v, given by (a, b, c), has absolute value √(a^{2} + b^{2} + c^{2}) . Absolute value is symbolized by vertical bars, as in x, z, or v, and obeys certain fundamental properties, such as a · b = a · b and a + b ≤ a + b.* * *
Universalium. 2010.
Look at other dictionaries:
absolute value — n. 1. the magnitude of a real number, disregarding its positive or negative sign [the absolute value of 4 or +4, written  4 or +4, is 4] 2. the magnitude of a complex number; modulus … English World dictionary
absolute value — value of a number expressed as a positive number (i.e. 23 has an absolute value of 23) … English contemporary dictionary
Absolute value — For the philosophical term, see Value (ethics). For the Akrobatik album, see Absolute Value (album). In mathematics, the absolute value (or modulus) a of a real number a is the numerical value of a without regard to its sign. So, for example,… … Wikipedia
Absolute Value — A business valuation method that uses discounted cash flow analysis to determine a company s financial worth. The absolute value method differs from the relative value models that examine what a company is worth compared to its competitors.… … Investment dictionary
absolute value — ab′solute val′ue n. 1) the magnitude of a quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as 3 or −3 is three 2) the square root of the sum of the… … From formal English to slang
absolute value — absoliučioji vertė statusas T sritis fizika atitikmenys: angl. absolute value vok. Absolutwert, m rus. абсолютное значение, n pranc. valeur absolue, f … Fizikos terminų žodynas
absolute value — skaičiaus modulis statusas T sritis informatika apibrėžtis Matematinė sąvoka, reiškianti skaičiaus absoliutinę reikšmę x, kuri apibrėžiama taip: Iliustraciją žr. priede. Skaičiaus modulis visuomet didesnis arba lygus nuliui. Modulį galima gauti … Enciklopedinis kompiuterijos žodynas
absolute value — noun Date: 1889 1. a nonnegative number equal in numerical value to a given real number 2. the positive square root of the sum of the squares of the real and imaginary parts of a complex number … New Collegiate Dictionary
absolute value — noun a) For a real number, its numerical value without regard to its sign; formally, 1 times the number if the number is negative, and the number unmodified if it is zero or positive. b) For a complex number, the … Wiktionary
absolute value — noun 1》 Mathematics the magnitude of a real number without regard to its sign. 2》 technical the actual magnitude of a numerical value or measurement, irrespective of its relation to other values … English new terms dictionary