OCTONION MULTIPLICATION Meaning and
Definition
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Octonion multiplication refers to the mathematical operation performed on octonions, which are elements of the octonion algebra, an eight-dimensional non-associative algebra. The octonion algebra extends the concept of complex numbers and quaternions, possessing additional properties and rules that make it particularly intriguing and important in theoretical physics and advanced mathematics.
The octonion multiplication operation involves the combination and manipulation of octonions to obtain new octonions. It differs from the more familiar multiplication operations of complex numbers and quaternions due to its non-associativity, meaning that the order of multiplication matters. When two octonions are multiplied together, the result is not necessarily the same as the product obtained by reversing the order of multiplication.
The rules of octonion multiplication are governed by a set of specific properties that include non-commutativity, non-associativity, and zero divisors. These properties are essential when working with octonions and make the octonion algebra distinct from other algebras.
Octonion multiplication can be visualized using a multiplication table that shows all the possible combinations of multiplying different octonions together. Due to the complexity and non-trivial nature of octonions, their multiplication table exhibits intricate patterns and relationships, which have attracted substantial attention and study in the field of algebraic structures and their applications in mathematical physics.
Etymology of OCTONION MULTIPLICATION
The word "octonion" comes from the Latin roots "octo" meaning "eight" and "onion" meaning "organized" or "ordered". In mathematics, octonions refer to an eight-dimensional algebraic structure that extends the concept of complex numbers and quaternions.
The term "multiplication" originated from the Latin word "multiplicare", which means "to multiply" or "to increase". It refers to the mathematical operation of combining two or more numbers to obtain their product. In the context of octonions, the term "multiplication" denotes the specific rules and operations defined for this algebraic structure.
