Dual Number
In linear algebra, the dual numbers (or parabolic numbers) extend the real numbers by adjoining one new element ε with the property ε2 = 0 (ε is nilpotent). The collection of dual numbers forms a particular two-dimensional commutative unital associative algebra over the real numbers. Every dual number has the form z = a + bε with a and b uniquely determined real numbers. The plane of all dual numbers is an "alternative complex plane" that complements the ordinary complex number plane C and the motor plane D of split-complex numbers.
Read more about Dual Number: Linear Representation, Geometry, Algebraic Properties, Generalization, Differentiation, Superspace, Division, Exponentiation
Other articles related to "dual number, dual, number, numbers":
... Dual number survived until 14th - 15th century with some slight changes first person -vě > *-wie > -wa (due to the influence of the first person masculine dual dwa konja) (two horses) ... person to be differentiated from the second person singular) In the 16th century dual number disappeared from the literary language ... It has been preserved in a number of dialects but the meaning of words in the dual number is equal to their blending in plural ...
... The third factor affecting noun declension is number ... the example masculine animate noun muž (man) For the number one, the singular number is used jeden muž ... For the numbers 2, 3, and 4, any case may be used, depending on the function of the noun in the sentence dva muži (nominative) ...
... Exponentiation of dual numbers follows the general rule. ...
... The dual number has its specific inflections, that are similar with plural inflections with some specific differences Nominative, accusative or vocative masculine words end with -(i)u, feminine with -i Genitive ... -(i)am, -iem, -(i)om, -ėm, -im in the dual respectively Instrumental has the same inflections as the dual dative, but they are pronounced in different intonation ...
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