Abstract
In this paper we introduce the Jacobsthal quaternions and the Jacobsthal–Lucas quaternions and give some of their properties. We derive the relations between Jacobsthal quaternions and Jacobsthal–Lucas quaternions and we give the matrix representation of these quaternions.
Highlights
Let H be the set of quaternions q of the form q = a + bi + cj + dk, (1)
The conjugate of a quaternion is defined by q∗ = (a + bi + cj + dk)∗ = a − bi − cj − dk
Numbers of the Fibonacci type are defined by the second-order linear recurrence relation of the form an = b1an−1 + b2an−2, where bi ∈ N, i = 1, 2
Summary
Let H be the set of quaternions q of the form q = a + bi + cj + dk, (1) If q1 = a1 + b1i + c1j + d1k and q2 = a2 + b2i + c2j + d2k are any two quaternions equality, addition, substraction and multiplication by scalar are defined. The conjugate of a quaternion is defined by q∗ = (a + bi + cj + dk)∗ = a − bi − cj − dk. The norm of a quaternion is defined by
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