Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript is mathematically rigorous and original in its approach. Some minor changes are required. Please see the report.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I have a number of minor remarks as follows.

1. Put grs (from group rotation-stretch) in Roman, i.e. grs.
2. Use {rrrr} in the LaTeX command for the arrays instead of {cccc} in (6), Ex. 2, Ex. 3, p. 8, table at p. 9.
3. On p. 3 delete a dot in the last element of the vector J.
4. Start words in titles of books with capital (e.g. in [10], [14], etc.).
5. Where references [22] and [25] are submitted?
6. Put titles of journals in Italic.
7. Give doi whenever possible.
8. The phrase "alchemical approaches" seems exaggerated and should be deleted.
9. Put horizontal spaces by the command ~, e.g. after 1843 and 1819 at p. 1, etc.
10. There is an empty [ ] at p. 9.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper studies the problem of ' quaternion without imaginary number or vector representation of quaternion ', which is a problem of academic value and can be considered to be accepted and published. However, it can be improved from the following aspects : 
 
1. The abstract is not standard enough. The innovation and main content of the paper should be introduced. 
 
2, Keywords are not standardized, keywords should be concise, so that readers clearly understand the key issues to be studied. 
 
3. The research background is not standardized enough. The author did not analyze and summarize the research background and existing problems in this field. 
 
4, References cited order confusion, lack of logic ; 
 
5, the paper lacks examples to verify and analyze the methods or principles proposed in the article.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

From the revised paper, the paper did not meet the expected requirements, it is recommended that the author continue to modify the paper.

Author Response

Thank you for your time. Somewhere in the revision process, some additional proves  and the additional       Concluding remarks     section I had added in the meantime were lost. I have now re-inserted it all. 

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have revised the paper in the light of the reviewers' comments and suggestions. The current version of the paper is acceptable for publication.