**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* + *b*ε 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**

...

**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) ...

**Dual Number**- Exponentiation

... Exponentiation of dual numbers follows the general rule. ...

**Dual Number**

... 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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—Michel de Montaigne (1533–1592)

“Thee for my recitative,

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declining,

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—Walt Whitman (1819–1892)