Quaternion algebra{\\mathbb{H}}is a noncommutative associative algebra. In recent years, quaternionic Fourier analysis has received increasing attention due to its applications in signal analysis and image processing. This paper addresses conjugate phase retrieval problem in the quaternion Euclidean space...
As astounding as it may still seem to many, Bell’s theorems do not prove nonlocality. Non separable multipartite objects exist classically, meaning w
Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and are anti-commuting square roots of with , , . While they are non-commutative, they do keep many other properties of the complex numbers: ...
Right multplication of this quaternion then corresponds to various natural operations on this unit tangent vector: Right multiplying by does not affect the location of the tangent vector, but rotates the tangent vector anticlockwise by in the direction of the orthogonal tangent vector , as it ...
While they are non-commutative, they do keep many other properties of the complex numbers: Being non-commutative, the quaternions do not form a field. However, they are still a skew field (or division ring): multiplication is associative, and every non-zero quaternion has a unique ...