Page "Dual number" Paragraph 0

In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε < sup > 2 </ sup > = 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 plane of split-complex numbers.