Matrix Mathematics: A Second Course in Linear Algebra

by Stephan Ramon Garcia, Roger A. Horn

Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.

Genres: Mathematics

500 pages, Kindle Edition

Published May 25, 2023

Reviews

[Dr. Garrett · Rating 5 out of 5]

I'm writing a few sentences regarding the importance of this manuscript for the scientific community. Why I like this manuscript.

From the importance of this article for the scientific community, we can mention the research on the widely used and attractive structure of matrices. I am interested in this article because matrices are one of the most beautiful topics in mathematics. The topic of matrices is interesting in itself, but matrices have many applications in other fields. Therefore, any progress in the field of matrices can lead to a significant change in the progress of science, because mathematics topics that use matrices are one of the most popular and famous topics in mathematics and are among the best topics. For example, when we examine graphs with the matrix tool, we have chosen one of the most famous and most reliable branches called algebraic graph theory as a field. In general, when the name of the matrix is ​​seen in the title of the research, many scientific research scientists are encouraged to follow the research and study it by just seeing the name of the matrix and without paying attention to other things.

The title of the article is suitable.

The title of the article is appropriate. Because in the title of the article, both the field of research and the research tool can be seen. The title of the article is also beautiful and professional because the title refers to the generalized tool, which indicates the long history of the research and the superior tool of this research. Nevertheless, the author's effort to provide a comprehensive and accurate statement to provide the title of the article is commendable. This title of the article removes ambiguity for the reader and gives an attractive understanding of the research topic. The use of beautiful literature to attract the reader in choosing the word of study and the use of generalized adjectives to build confidence about the accuracy of the structure of the article are impressive.

The abstract of the article is comprehensive.

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Subsections and structure of the manuscript are appropriate.

The structure of the article is appropriate and the formation of sections and subsections are in accordance with scientific standards. The topics of each section and sub-section correspond to the title of the section and the placement of the sections is also appropriate.

I'm writing a few sentences regarding the scientific correctness of this manuscript. Why I think that this manuscript is scientifically robust and technically sound.

Technically and scientifically, by observing the details of the proofs and references, there is no doubt about the correctness of the article. The contents and proofs are explained step by step in detail. In the introduction, the validity of the article and previous research is mentioned, which makes the technical importance of the article flourish for the scientific community. The topic of matrices is one of the difficult and beautiful topics, which indicates that this article is scientifically robust. This research has used the tool of generalized numbers and has created many attractive relationships between concepts.

The references are sufficient and recent.

The references are among recent sources and their number is suitable. The references used include scientific research articles published in reputable journals, and references to unpublished articles, drafts, submitted articles, preprints, and articles published in non-authoritative, low-credibility, or unpublished journals have been avoided. This type of author's attitude in choosing references is not only prestigious but also educational and praiseworthy for the reader. All sources are used in the text of the article and referenced in the text. References parallel to each other have been avoided and each reference is unique in terms of structure and selection.

The language/English quality of the article is suitable for scholarly communications.

The quality of the English language of the article is suitable for research-oriented communication. Scholarly communication requires that literature be accurate and beautiful. This is considered in writing the article.

Optional/General comments

The topic of matrices is one of the most respected topics in mathematics. It has many applications in theoretical and applied sciences. Because one of the study tools in science is modeling and converting concepts into matrices. This article requires the need to study the matrices theoretically. This research has given an immediate answer to this need and with a comprehensive and continuous study, it tries to form a superior study according to the previous research.

There is no ethical issues in this manuscript. There is no competing interest issues in this manuscript. Plagiarism isn't suspected. I gave overall marks I want to give to this manuscript (Highest: 10 Lowest: 0): 10.