# Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

## Abstract

In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.

- Authors:

- Department of Mathematics, Linyi University, Linyi, Shandong 276005 (China)
- (China)

- Publication Date:

- OSTI Identifier:
- 22479588

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; MATRICES; QUANTUM MECHANICS

### Citation Formats

```
Jiang, Tongsong, E-mail: jiangtongsong@sina.com, Department of Mathematics, Heze University, Heze, Shandong 274015, Jiang, Ziwu, and Zhang, Zhaozhong.
```*Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics*. United States: N. p., 2015.
Web. doi:10.1063/1.4928935.

```
Jiang, Tongsong, E-mail: jiangtongsong@sina.com, Department of Mathematics, Heze University, Heze, Shandong 274015, Jiang, Ziwu, & Zhang, Zhaozhong.
```*Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics*. United States. doi:10.1063/1.4928935.

```
Jiang, Tongsong, E-mail: jiangtongsong@sina.com, Department of Mathematics, Heze University, Heze, Shandong 274015, Jiang, Ziwu, and Zhang, Zhaozhong. Sat .
"Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics". United States. doi:10.1063/1.4928935.
```

```
@article{osti_22479588,
```

title = {Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics},

author = {Jiang, Tongsong, E-mail: jiangtongsong@sina.com and Department of Mathematics, Heze University, Heze, Shandong 274015 and Jiang, Ziwu and Zhang, Zhaozhong},

abstractNote = {In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.},

doi = {10.1063/1.4928935},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 8,

volume = 56,

place = {United States},

year = {2015},

month = {8}

}

DOI: 10.1063/1.4928935

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