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In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical ...
The numerical range is the range of the Rayleigh quotient. (Hausdorff–Toeplitz theorem) The numerical range is convex and compact.(+) = + {} for all square matrix and complex numbers and .
Older books, when they use the word "range", tend to use it to mean what is now called the codomain. [1] More modern books, if they use the word "range" at all, generally use it to mean what is now called the image. [2] To avoid any confusion, a number of modern books don't use the word "range" at all. [3]
R – real numbers. ran – range of a function. rank – rank of a matrix. (Also written as rk.) Re – real part of a complex number. [2] (Also written.) resp – respectively. RHS – right-hand side of an equation. rk – rank. (Also written as rank.) RMS, rms – root mean square. rng – non-unital ring. rot – rotor of a vector field.
Range (statistics), the difference between the highest and the lowest values in a set; Interval (mathematics), also called range, a set of real numbers that includes all numbers between any two numbers in the set; Column space, also called the range of a matrix, is the set of all possible linear combinations of the column vectors of the matrix
For example, "almost all real numbers are transcendental" because the algebraic real numbers form a countable subset of the real numbers with measure zero. One can also speak of "almost all" integers having a property to mean "all except finitely many", despite the integers not admitting a measure for which this agrees with the previous usage.
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Say (,) is equipped with its usual topology. Then the essential range of f is given by . = { >: < {: | | <}}. [7]: Definition 4.36 [8] [9]: cf. Exercise 6.11 In other words: The essential range of a complex-valued function is the set of all complex numbers z such that the inverse image of each ε-neighbourhood of z under f has positive measure.
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