Algebra

Small Identity with Bright Life

Authors: Alexander Komarow
Comments: 12 Pages.

Given Hamilton quaternion definition in modern Geometric (Clifford) Algebra language we point out a simple identity that leads to a theorem: any quaternion function f(q) can be expressed as a linear function f(q) = Aq +B with real functions A,B of invariants Trace and square norm N of q (or eigenvalues). We develop an explicit closed-form formulas to calculate these functions using three different methods. That might be useful to get the explicit closed form of infinite polynomials of q, Fibonacci-Lucas series, BCH (Baker—Campbell—Hausdorff formula ) as examples.
Category: Algebra