French translation for "octonion"

octonion

Example Sentences:

	1.	There are corresponding split octonion algebras over any field F. The octonions and the split-octonions can be obtained from the Cayley–Dickson construction by defining a multiplication on pairs of quaternions. Les octonions et les octonions déployés peuvent être obtenus par la construction de Cayley-Dickson (en) en définissant une multiplication sur les paires de quaternions.
	2.	An algebraic symmetry is lost with each increase in dimensionality: quaternion multiplication is not commutative, octonion multiplication is non-associative, and the norm of sedenions is not multiplicative. Augmenter la dimension introduit des complications algébriques : la multiplication des quaternions n’est plus commutative, la multiplication des octonions est, de plus, non associative et la norme sur les sédénions n'est pas multiplicative.
	3.	Write an octonion x {\displaystyle x} in the form x = ( a + v ) + ℓ ( b + w ) {\displaystyle x=(a+\mathbf {v} )+\ell (b+\mathbf {w} )} where a {\displaystyle a} and b {\displaystyle b} are real numbers and v and w are pure imaginary quaternions regarded as vectors in R3. Écrivons un octonion x sous la forme x = ( a + a ) + ℓ ( b + b )
	4.	After identifying ℝ7 with the imaginary octonions (the orthogonal complement of the real line in O), the cross product is given in terms of octonion multiplication by x × y = I m ( x y ) = 1 2 ( x y − y x ) . {\displaystyle \mathbf {x} \times \mathbf {y} =\mathrm {Im} (\mathbf {xy} )={\frac {1}{2}}(\mathbf {xy} -\mathbf {yx} ).} Conversely, suppose V is a 7-dimensional Euclidean space with a given cross product. Identifiant R7 aux octonions imaginaires (le complément orthogonal de la droite des réels dans O), le produit vectoriel est donné (en utilisant la multiplication des octonions) par x × y = I m ( x y ) = 1 2 ( x y − y x ) .

Similar Words：

"octolasion lacteum" French translation, "octomania/sandbox" French translation, "octomylodon" French translation, "octon, hérault" French translation, "octonary" French translation, "octonion algebra" French translation, "octonoba" French translation, "octonoba sinensis" French translation, "octonoba yaeyamensis" French translation