Matches in DBpedia 2016-04 for { ?s ?p "In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras. They are useful composition algebras frequently applied in mathematical physics.The Cayley–Dickson construction defines a new algebra based on the direct sum of an algebra with itself, with multiplication defined in a specific way and an involution known as conjugation. The product of an element and its conjugate (or sometimes the square root of this) is called the norm.The symmetries of the real field disappear as the Cayley–Dickson construction is repeatedly applied: first losing order, then commutativity of multiplication, and next associativity of multiplication.More generally, the Cayley–Dickson construction takes any algebra with involution to another algebra with involution of twice the dimension."@en }
Showing triples 1 to 2 of
2
with 100 triples per page.
- Cayley–Dickson_construction abstract "In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras. They are useful composition algebras frequently applied in mathematical physics.The Cayley–Dickson construction defines a new algebra based on the direct sum of an algebra with itself, with multiplication defined in a specific way and an involution known as conjugation. The product of an element and its conjugate (or sometimes the square root of this) is called the norm.The symmetries of the real field disappear as the Cayley–Dickson construction is repeatedly applied: first losing order, then commutativity of multiplication, and next associativity of multiplication.More generally, the Cayley–Dickson construction takes any algebra with involution to another algebra with involution of twice the dimension.".
- Q1756828 abstract "In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras. They are useful composition algebras frequently applied in mathematical physics.The Cayley–Dickson construction defines a new algebra based on the direct sum of an algebra with itself, with multiplication defined in a specific way and an involution known as conjugation. The product of an element and its conjugate (or sometimes the square root of this) is called the norm.The symmetries of the real field disappear as the Cayley–Dickson construction is repeatedly applied: first losing order, then commutativity of multiplication, and next associativity of multiplication.More generally, the Cayley–Dickson construction takes any algebra with involution to another algebra with involution of twice the dimension.".