We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f ,g. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by f ,g, or by only one pure unit quaternion f , comment on their geometric meaning, and establish invers...

The practical and accurate computation of the singular value decomposition of a quaternion matrix is of importance in vector signal processing using quaternions. We present a Jacobi algorithm for computing such an SVD, and discuss its utility and accuracy. The algorithm is included in an open-source Matlab toolbox for quaternions where it serves as an accurate reference implementation.

Abstract The aim of this article is to investigate two new classes quaternions, namely, balancing and Lucas-balancing quaternions that are based on numbers, respectively. Further, some identities including Binet’s formulas, summation Catalan’s identity, etc. concerning these also established.

In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of numbers. We examine some identities quaternions. introduce their basic definitions and properties. give Binet’s formula, Cassini’s identity, Catalan’s d’Ocagne generating functions, exponential functions also relations between Jacobsthal

In this paper, with the help of finite operators and Fibonacci numbers, we define a new family quaternions whose components are operator numbers. We also provide some properties these types quaternions. Moreover, derive many identities related to by using matrix representations.