Guidance for Electronic Journal of Linear Algebra (ELA) Refereeing Process


This document provides guidance to referees (as well as editorial board members who oversee this process) on the standards and decision making for papers submitted to ELA.


ELA’s Editorial Board believes that high standards for publication are of benefit to the authors, the journal, and the Linear Algebra community. Referees can help uphold these high standards, as well as help the authors produce better papers in the future. The standards of ELA are comparable to those of other leading journals in Linear Algebra, for example, Linear Algebra and Its Applications, Linear and Multilinear Algebra or SIAM Journal on Matrix Analysis and Applications.


ELA’s Editorial System (OJS) is used by editors and referees to record all their actions, communications and recommendations. The editors take all measures to preserve the anonymity of referees to the author(s).


A. Judging the Quality of a Paper

ELA considers primarily original research papers, but also encourages survey papers. The latter, by their very

nature, need not contain new results and should be evaluated according to their ability to provide a critical assessment and comparison of existing work, to stimulate new research and interest on a topic, as well as to summarize well-known and less known results for the benefit of future research.


ELA’s Editorial Board asks referees to consider (some or all of) the following qualities and questions in judging whether a research paper is publishable in ELA or not:


(i) Correctness of results and proofs

ELA adopts the Halmos standard: a referee is not required to certify the correctness of the results in the paper, but does need to indicate whether or not the results are plausible and seem correct. As a referee, you should spend some time in error-detection (e.g., identify misstated results or logical errors) and suggest minor fixes. You are not expected, however, to do the research intended by the author(s).


(ii) Significance, innovation, interest or timeliness

  • Are the mathematical questions studied in the paper of some significance in your opinion? (Problems with obvious or simple solutions, or results that are minor improvements of known results will not be published.)

  • Are the results original and innovative? (Simple extensions or combinations of known results will not be published.)

  • Are the proof techniques new, or do they provide a novel use of known techniques?

  • Does the paper provide motivation and put the results into a proper framework?

  • Does the paper address a problem of recent or historical interest?

  • Will the results of the paper provide new insights to ongoing research by others?


(iii) Succinctness and accessibility

  • Do the proofs and the exposition provide an appropriate level of detail?

  • Is the material accessible for the typical International Linear Algebra Society (ILAS) member or ELA reader?

  • Are appropriate references to background material provided?


(iv) Readability, style and elegance

  • Will the reader be able to unpack the results in the paper with a reasonable amount of effort?

  • Is the exposition well-structured with proper use of scholarly vocabulary and grammar?

  • Is it evident that care has been taken by the author(s) in all aspects of the manuscript’s preparation?






B. The Recommendation

Recommendations for papers fall into the following typical categories:


  1. The effort or results constitute a major contribution, perhaps with some improvements or revisions

  2. The paper is acceptable, perhaps with some improvements or revisions

  3. The subject is out of ELA's scope

  4. Results are published elsewhere

  5. Results are not of high enough level of novelty, significance or difficulty

  6. The paper is tedious, or there is too much in the literature on the same subject

  7. The paper is thin in new results or does not represent sufficient progress

  8. The paper contains major errors

  9. The exposition of the material is poor



C. The Referee Report

Referees can communicate (privately) with editors by initiating an OJS Review Discussion, in order to seek further guidance or express concerns. Referees are asked to not communicate directly with authors without the prior knowledge of the handling editor. Referees are asked to prepare their reports to the author(s) and editor so that it


  • clearly indicates a recommendation,

  • identifies specific ways that the paper can be improved, if any, and

  • provides comments that can benefit the author(s) by guiding them toward excellence.


Categories 4 and 7 do not apply to survey papers. Papers in categories 3-9 above will be rejected. A recommendation based on category 3 should be communicated very quickly to the editor handling the paper. If the substance of the paper is considered significant enough, then the author(s) of papers in categories 1-2 may be asked to provide a minor or major revision. We encourage referees to push authors to do better; so if you feel there is room for improvement, please do not put a paper in category 1. For papers in categories 1-2, help the author(s) and ELA’s managing editors team identify and correct typographical and linguistic errors to a reasonable extent.


Concluding Remarks

ELA editors expect referees to respect the guidelines above, but also to interpret and adjust them within reason and according to their professional experiences. For example, referees being consulted because of their expertise in a mathematical or scientific field other than linear algebra are expected to express their opinion on the impact of the results in their fields of expertise.


Typically, ELA expects reports on original submissions within three months. For relative minor revisions, a report is expected within one month. In the network of scholarly publication, the refereeing process lies upon the "critical path". Timely, thoughtful reports, allow good mathematics to be made available to the community sooner. If circumstances arise that prevent a referee from adhering to a deadline, ELA should be informed as soon as possible.


The refereeing service is greatly appreciated by ELA and ILAS, and helps make our community stronger and more highly respected.