mathematics, the absolute value or modulus of a real number x {\displaystyle x} , denoted | x | {\displaystyle |x|} , is the non-negative value of x {\displaystyle...

absolute value in Wiktionary, the free dictionary. The absolute value is a value of a real number. Absolute value may also refer to: Absolute value (algebra)...

existence of absolute values, which can also be termed noumenal values (and not to be confused with mathematical absolute value). An absolute value can be described...

In algebra, an absolute value is a function that generalizes the usual absolute value. More precisely, if D is a field or (more generally) an integral...

following properties, where | s | {\displaystyle |s|} denotes the usual absolute value of a scalar s {\displaystyle s} : Subadditivity/Triangle inequality:...

{\displaystyle x_{i}} the true value. Alternative formulations may include relative frequencies as weight factors. The mean absolute error uses the same scale...

Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical...

where At is the actual value and Ft is the forecast value. Their difference is divided by the actual value At. The absolute value of this ratio is summed...

absolute difference of two real numbers x {\displaystyle x} and y {\displaystyle y} is given by | x − y | {\displaystyle |x-y|} , the absolute value of...

homogeneous function that is not homogeneous. A special case is the absolute value of real numbers. The quotient of two homogeneous polynomials of the...

Residual value also known as salvage value describes the future value of a good in terms of absolute value in monetary terms after depreciation, and it...

defined by its geometric polar coordinates: the radius is called the absolute value of the complex number, while the angle from the positive real axis is...

analogue of the usual absolute value. Whereas the completion of the rational numbers with respect to the usual absolute value results in the real numbers...

nor the mean-value theorem hold for the symmetric derivative; some similar but weaker statements have been proved. For the absolute value function f (...

principal ways: as an absolute error, which denotes the direct numerical magnitude of this discrepancy irrespective of the true value's scale, or as a relative...

MAD is the median of their absolute values. Consider the data (1, 1, 2, 2, 4, 6, 9). It has a median value of 2. The absolute deviations about 2 are (1...

function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, square-integrability...

difference: the deviation is positive when the observed value exceeds the reference value. The absolute value of the deviation indicates the size or magnitude...

religious values. Further categorizations distinguish absolute values from values that are relative to something else. Value realists state that values exist...

| n | {\displaystyle |n|} is the absolute value of n {\displaystyle n} . Negation is used to find the negative value of a single number. Here are some...

mean absolute difference (univariate) is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn...

"exponential valuation" or "non-Archimedean absolute value" or "ultrametric absolute value"; our "absolute value" (satisfying the triangle inequality) is...

actual value and Ft is the forecast value. The absolute difference between At and Ft is divided by half the sum of absolute values of the actual value At...

rank one valued fields and normed spaces over rank one valued fields as follows. Let K {\displaystyle K} be a field endowed with an absolute value function...

\end{array}}} Any real number can be expressed as the product of its absolute value and its sign: x = | x | sgn ⁡ x . {\displaystyle x=|x|\operatorname...

necessarily finite. This article uses the former definition. Given such an absolute value on a field K, the following topology can be defined on K: for a positive...

example in R 2 {\displaystyle \mathbb {R} ^{2}} ). The singular values are the absolute values of the eigenvalues of a normal matrix A, because the spectral...

&{\text{otherwise.}}\end{cases}}} The Huber loss is the convolution of the absolute value function with the rectangular function, scaled and translated. Thus...

the usual absolute value of their difference. The corresponding mapping to an additive group would be the logarithm of the absolute value, although this...

the interval [0, +∞). On the negative numbers, numbers with greater absolute value have greater squares, so the square is a monotonically decreasing function...