Similarity of hybrid numbers

Abstract

The set of hybrid numbers 𝕂 is a noncommutative number system that unified and generalized the complex, dual, and double (hyperbolic) numbers with the relation ih =−hi=ε+i. Two hybrid numbers p and q are said to be similar if there exist a nonlightlike hybrid number x satisfying the equality x−1qx = p. And, it is denoted by p∼q. In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations px = xq and qx−xp = c for boldp,boldq,boldc∈𝕂bold.

Hybrinomials related to hyper-Leonardo numbers

“…In recent years, hybrid numbers have been the subject of research [12][13][14][15][16][17][18][19]. Özdemir [19] introduced hybrid numbers, as a generalization of complex, hyperbolic and dual numbers, sets by:…”

De Moivre’s and Euler Formulas for Matrices of Hybrid Numbers

“…Here cos g θ and sin g θ denote the cosine and sine Galilean trigonometric functions, respectively. In [14], the left matrix representation of the hybrid number Z is given by…”

“…In [14], the authors studied the concept of similarity for hybrid numbers by using the solutions of some linear equations. In [15], the author gave a new method for finding nth roots of a 2 × 2 real matrix with the help of hybrid numbers.…”

Hyper-Leonardo Hybrinomials

“…Hybrid numbers have been the subject of much research recently [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Szynal-Liana and Wloch [16] defined the 𝑛-th Fibonacci hybrid number as…”