Algebraic techniques for eigenvalues and eigenvectors of a nectarine matrix in nectarine algebra. (22nd October 2022)

• Record Type: Journal Article
• Authors: Guo, Zhenwei; Jiang, Tongsong; Jiang, Chuan; Wang, Gang
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 4(2023)
• Page Start: 4751
• Page End: 4762
• Publication Date: 2022-10-22
• Subjects: eigenvector -- nectarine -- nectarine matrix -- real representation matrix -- right eigenvalue; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8801
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A nectarine was introduced in 2014 by Bernd Schmeikal in the form of q = q 1 + q 2 i + q 3 j + q 4 k $$ q={q}_1+{q}_2\mathrm{i}+{q}_3\mathrm{j}+{q}_4\mathrm{k} $$, i 2 = k 2 = ijk = 1, j 2 = − 1 $$ {\mathrm{i}}^2={\mathrm{k}}^2=\mathrm{ijk}=1, {\mathrm{j}}^2=-1 $$, and ij = − ji = k, jk = − kj = i, ik = − ki = j $$ \mathrm{ij}=-\mathrm{ji}=\mathrm{k}, \mathrm{jk}=-\mathrm{kj}=\mathrm{i}, \mathrm{ik}=-\mathrm{ki}=\mathrm{j} $$, in which q 1, q 2, q 3, q 4 $$ {q}_1, {q}_2, {q}_3, {q}_4 $$ are real numbers. This paper studies the problems of right eigenvalues and eigenvectors of a nectarine matrix by means of a real representation matrix of the nectarine matrix and derives algebraic techniques for the right eigenvalues and eigenvectors of the nectarine matrix.