multiplication
Multiplication is a mathematical operation
in which two or more numbers are added up to themselves by a factor of other numbers. For example, 2×3=2+2+2=3+3=6. The numbers may be real, imaginary
or complex, they may be integers or fractions. Among real numbers, if an odd number
of multiplicands are negative, the overall result is negative; if an even number of multiplicands are negative, the overall result is positive. Two examples: (-3)×(-5)=15; (-2)×(-3)×(-5)=(-30).
The usual operator is the cross with its four arms of equal length pointing northeast, northwest, southeast and southwest: ×. Other options are the central dot ⋅ and the tacit multiplication operator. In many computer programming languages the asterisk is often used as it is almost always available on the keyboard (Shift-8 in most American layouts, as well as dedicated key if the keyboard has a numeric keypad), and this is the operator likely to be used in a computer implementation of a reverse Polish notation calculator. In Mathematica, the space can sometimes function as a multiplication operator, but more experienced users warn novices not to rely on this feature.
Just as with addition, multiplication is commutative: xyz=xzy=yxz, etc.
The iterative operator is the Greek capital letter pi:
n∏i=1ai, |
which is a compact way of writing a1×a2×…×an.
Multiplication of complex numbers is helped by the following identity: (a+bi)×(x+yi)=(ax-by)+(ay+bx)i. To give three examples: (17+29i)(11+38i)=-915+965i (the result has both real and imaginary parts), (1+2i)(1-2i)=5 (the result is a real prime) and (4+7i)(7+4i)=65i (the result has only an imaginary part).
Title | multiplication |
---|---|
Canonical name | Multiplication |
Date of creation | 2013-03-22 16:35:37 |
Last modified on | 2013-03-22 16:35:37 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 10 |
Author | PrimeFan (13766) |
Entry type | Definition |
Classification | msc 00A06 |
Classification | msc 11B25 |
Classification | msc 00A05 |
Related topic | Product |
Related topic | ProductOfNegativeNumbers |
Related topic | FactorsWithMinusSign |