Kvaternionteina

Kvaternionteina is a term found in some regional mathematical texts to denote a quaternion-like four-dimensional hypercomplex number system. It is not a standard term in mainstream mathematics, and its exact definition varies between sources. In many accounts it serves as a pedagogical variant of the ordinary quaternions.

Algebraic structure: Kvaternionteina are described as a real four-dimensional algebra generated by 1, i, j, k, with multiplication rules modeled on quaternions. In the typical formulation, i^2 = j^2 = k^2 = -1 and ij = k, jk = i, ki = j, with reverse products giving minus signs. Some texts introduce variant sign conventions that yield related algebras.

Representation and computation: An element is written q = a + bi + cj + dk with real a, b, c, d. Multiplication follows the stated rules and can be realized by expansion or by matrix representations that preserve the algebraic structure, enabling practical calculations much as ordinary quaternions do for rotations.

Properties and applications: Kvaternionteina are typically non-commutative and associative, and many descriptions include a conjugation and a norm that generalize the complex modulus. When the variant aligns with quaternion-like rules, the norm is multiplicative and inverses exist for nonzero elements, supporting rotation-like interpretations in graphics or robotics.

Notes: Because kvaternionteina is not universally standardized, readers should consult local texts for the exact conventions used in a given work. The term may be used to illustrate quaternion concepts or as a regional label for a quaternion-like algebra rather than as a distinct, widely adopted system.