This article is about the absolute value of real and complex numbers. For other absolute values in mathematics, see Absolute value (algebra). For other uses, see Absolute value (disambiguation).
The graph of the absolute value function for real numbersThe absolute value of a number may be thought of as its distance from zero.
In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.
Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.
mathematics, the absolutevalue or modulus of a real number x {\displaystyle x} , denoted | x | {\displaystyle |x|} , is the non-negative value of x {\displaystyle...
where At is the actual value and Ft is the forecast value. Their difference is divided by the actual value At. The absolutevalue of this ratio is summed...
{\displaystyle x_{i}} the true value. Alternative formulations may include relative frequencies as weight factors. The mean absolute error uses the same scale...
homogeneous function that is not homogeneous. A special case is the absolutevalue of real numbers. The quotient of two homogeneous polynomials of the...
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolutevalues (LAV), is a statistical...
inconceivable quantity Absolute magnitude, the brightness of a star Absolutevalue, a notion in mathematics, commonly a number's numerical value without regard...
converge absolutely (or to be absolutely convergent) if the sum of the absolutevalues of the summands is finite. More precisely, a real or complex series...
defined by its geometric polar coordinates: the radius is called the absolutevalue of the complex number, while the angle from the positive real axis is...
mean absolute difference (univariate) is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn...
Residual value is one of the constituents of a leasing calculus or operation. It describes the future value of a good in terms of absolutevalue in monetary...
nor the mean-value theorem hold for the symmetric derivative; some similar but weaker statements have been proved. For the absolutevalue function f (...
the usual absolutevalue of their difference. The corresponding mapping to an additive group would be the logarithm of the absolutevalue, although this...
absolute difference of two real numbers x {\displaystyle x} and y {\displaystyle y} is given by | x − y | {\displaystyle |x-y|} , the absolutevalue of...
quantity: both magnitude and direction are needed to define it. The scalar absolutevalue (magnitude) of velocity is called speed, being a coherent derived unit...
where | n | {\displaystyle |n|} is the absolutevalue of n {\displaystyle n} . This is used to find the negative value of a single number. Here are some examples:...
{a\times d}={c\times b}.} If the absolutevalue of m is greater than n (supposed to be positive), then the absolutevalue of the fraction is greater than 1...
is the signed measure of its projection on the primary axis, whose absolutevalue is the distance between the projection and the origin of the axis, and...
tendency or any reference value related to the given data set. AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated...
In calculus, the squeeze theorem (also known as the sandwich theorem, among other names) is a theorem regarding the limit of a function that is trapped...
MAD is the median of their absolutevalues. Consider the data (1, 1, 2, 2, 4, 6, 9). It has a median value of 2. The absolute deviations about 2 are (1...
Absolute zero is the lowest limit of the thermodynamic temperature scale; a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum...
the average rectified value (ARV) of a quantity is the average of its absolutevalue. The average of a symmetric alternating value is zero and it is therefore...
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