OCTONIONICS Meaning and
Definition
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Octonionics is a mathematical system that extends the concept of complex numbers and quaternions, introducing a new algebraic structure called octonions. It is a non-associative division algebra that operates in eight dimensions, and it is sometimes referred to as Cayley numbers. Octonionics is a highly specialized field within mathematics and plays a significant role in various branches of theoretical physics, such as string theory and quantum mechanics.
The octonions are built upon the concept of quaternion multiplication, which represents rotations in three-dimensional space. However, unlike quaternions, octonions have the property of non-associativity. This means that the order of multiplication affects the outcome, making it a more complex algebraic structure. Octonions also lack the property of commutativity, which means that the order of multiplication matters.
In octonionics, multiplication is defined by a set of rules and properties specific to octonions. These rules involve the combination of real numbers, imaginary units, and octonion basis elements to generate new elements within the algebra. Octonionics includes various mathematical properties, such as conjugation, norm, and inverse, which enable calculations and manipulations involving octonionic numbers.
Due to their intricate mathematical nature and applicability in theoretical physics, octonionics is primarily studied by mathematicians and physicists with a keen interest in advanced mathematical concepts and their potential implications in cosmology, quantum field theory, and gauge theories.
Common Misspellings for OCTONIONICS
- ictonionics
- kctonionics
- lctonionics
- pctonionics
- 0ctonionics
- 9ctonionics
- oxtonionics
- ovtonionics
- oftonionics
- odtonionics
- ocronionics
- ocfonionics
- ocgonionics
- ocyonionics
- oc6onionics
- oc5onionics
- octinionics
- octknionics
- octlnionics
- octpnionics
Etymology of OCTONIONICS
The word "octonionics" is derived from the term "octonion". The term "octonion" was coined by the mathematician Sir William Rowan Hamilton in 1843. It combines the Latin prefix "octo-" meaning "eight" with the term "onion" as a playful analogy to "quaternion", which refers to an extension of complex numbers to four dimensions. Just like a quaternion is composed of a real part and three imaginary parts, an octonion extends this concept to eight dimensions, with a real part and seven imaginary parts. The suffix "-ics" in "octonionics" simply denotes a field or branch of study related to octonions. Therefore, "octonionics" refers to the mathematical study and properties of octonions.
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