Ads
related to: quaternion identities worksheet printable 5th grade curriculum for homeschoolingteacherspayteachers.com has been visited by 100K+ users in the past month
- Lessons
Powerpoints, pdfs, and more to
support your classroom instruction.
- Try Easel
Level up learning with interactive,
self-grading TPT digital resources.
- Free Resources
Download printables for any topic
at no cost to you. See what's free!
- Packets
Perfect for independent work!
Browse our fun activity packs.
- Lessons
Search results
Results from the WOW.Com Content Network
The quaternion group has the unusual property of being Hamiltonian: Q 8 is non-abelian, but every subgroup is normal. [4] Every Hamiltonian group contains a copy of Q 8. [5] The quaternion group Q 8 and the dihedral group D 4 are the two smallest examples of a nilpotent non-abelian group.
The real quaternion 1 is the identity element. The real quaternions commute with all other quaternions, that is aq = qa for every quaternion q and every real quaternion a. In algebraic terminology this is to say that the field of real quaternions are the center of this quaternion algebra.
From this point of view, quaternionic representation of a group G is a group homomorphism φ: G → GL(V, H), the group of invertible quaternion-linear transformations of V. In particular, a quaternionic matrix representation of g assigns a square matrix of quaternions ρ(g) to each element g of G such that ρ(e) is the identity matrix and
Each quaternion has a tensor, which is a measure of its magnitude (in the same way as the length of a vector is a measure of a vectors' magnitude). When a quaternion is defined as the quotient of two vectors, its tensor is the ratio of the lengths of these vectors.
Comment: The proof of Euler's four-square identity is by simple algebraic evaluation. Quaternions derive from the four-square identity, which can be written as the product of two inner products of 4-dimensional vectors, yielding again an inner product of 4-dimensional vectors: (a·a)(b·b) = (a×b)·(a×b).
Such functions can be called functions of a quaternion variable just as functions of a real variable or a complex variable are called. As with complex and real analysis , it is possible to study the concepts of analyticity , holomorphy , harmonicity and conformality in the context of quaternions.
Ads
related to: quaternion identities worksheet printable 5th grade curriculum for homeschoolingteacherspayteachers.com has been visited by 100K+ users in the past month