SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E⁴₂

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

“…The authors showed the following result about the difference φ (a) − τ (b) in the last equation [16].…”

“…Unauthenticated Download Date | 5/10/18 10:03 PM where a = a 0 + a 1 i + a 2 j + a 3 k ∈ H S , [16]. It is nearby to identify a split quaternion a ∈ H S with a vector − → a ∈ R 4 2 (where R 4 2 is semi-Euclidean space [17]).…”

“…The split quaternions are a recently developing topic, since the split quaternions are used to express Lorentzian relations. Also, there are many studies on geometric and physical meaning of the split quaternions [16]- [17]. In [8], author studied equations ax = xb, ax = xb and x 2 = a, in algebras obtained by the Cayley-Dickson process.…”

“…The split quaternions are not commutative like real quaternions. But the set of split quaternions contains zero divisors, nilpotent and nontrivial idempotent elements [16]. The split quaternions are a recently developing topic, since the split quaternions are used to express Lorentzian relations.…”

Dual Pell Quaternions

“…Several authors worked on different quaternions and their generalizations [12][13][14][15][16][17][18][19][20][21][22] . Also, some authors worked on dual quaternions and their generalizations [2][3][4][5][6] as follows:…”