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The conjugate of a product of two quaternions is the product of the conjugates in the reverse order. That is, if p and q are quaternions, then (pq) ∗ = q ∗ p ∗, not p ∗ q ∗. The conjugation of a quaternion, in stark contrast to the complex setting, can be expressed with multiplication and addition of quaternions:
The product of a quaternion with its conjugate is its common norm. [63] The operation of taking the common norm of a quaternion is represented with the letter N. By definition the common norm is the product of a quaternion with its conjugate. It can be proven [64] [65] that common norm is equal to the square of the tensor of a quaternion ...
The word "conjugation" comes from the Latin coniugātiō, a calque of the Greek συζυγία (syzygia), literally "yoking together (horses into a team)". For examples of verbs and verb groups for each inflectional class, see the Wiktionary appendix pages for first conjugation , second conjugation , third conjugation , and fourth conjugation .
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
Most Latin verbs are regular and follow one of the five patterns below. [45] These are referred to as the 1st, 2nd, 3rd, and 4th conjugation, according to whether the infinitive ends in -āre, -ēre, -ere or -īre. [46] (Verbs like capiō are regarded as variations of the 3rd conjugation, with some forms like those of the 4th conjugation.)
This is a list of Latin words with derivatives in English language. Ancient orthography did not distinguish between i and j or between u and v. [1] Many modern works distinguish u from v but not i from j. In this article, both distinctions are shown as they are helpful when tracing the origin of English words. See also Latin phonology and ...
The main Latin tenses can be divided into two groups: the present system (also known as infectum tenses), consisting of the present, future, and imperfect; and the perfect system (also known as perfectum tenses), consisting of the perfect, future perfect, and pluperfect.
A direct formula for the conversion from a quaternion to Euler angles in any of the 12 possible sequences exists. [2] For the rest of this section, the formula for the sequence Body 3-2-1 will be shown. If the quaternion is properly normalized, the Euler angles can be obtained from the quaternions via the relations: