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Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas

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The essential reference book on matrices―now fully updated and expanded, with new material on scalar and vector mathematics

Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject.

Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more.

Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index.

  • Fully updated and expanded with new material on scalar and vector mathematics
  • Covers the latest results in matrix theory
  • Provides a list of symbols and a summary of conventions for easy and precise use
  • Includes an extensive bibliography with back-referencing plus an author index

14 reviews for Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas

  1. Lori King
    November 11, 2023
    5.0 out of 5 stars Accurate Depiction of Trauma Bonding
    This is an excellent book for anyone who suspects or knows they are in a trauma bond or toxic relationship and also a great resource for family or fri...More
    This is an excellent book for anyone who suspects or knows they are in a trauma bond or toxic relationship and also a great resource for family or friends trying to understand what their loved one is going through. Very accurate.
    Helpful? 0 0
    Adriana Zele
    September 20, 2023
    5.0 out of 5 stars Short but powerful
    Short and to the point, simple and clear explanations. I was able to read it in one sitting and found myself highlighting lots of stuff. May have to g...More
    Short and to the point, simple and clear explanations. I was able to read it in one sitting and found myself highlighting lots of stuff. May have to get it in paperback form.
    Helpful? 0 0
    GamingLady
    May 10, 2023
    5.0 out of 5 stars Tough life for those bonded
    Love it, it was written by someone whose been there, lots of feeling words, which narcissist never use. Written from the heart, honest. Thanks Lauren.
    Helpful? 0 0
    Lynette Zhang
    November 28, 2022
    5.0 out of 5 stars A great reference book for applied mathematicians
    If you work in an applied math-related area, and frequently need to figure out some matrix mathematics, you will benefit from this book.
    Helpful? 0 0
    Gaye Nesbitt
    October 21, 2022
    5.0 out of 5 stars Good book and easy to read in one day
    Great information on the subject and health issues
    Helpful? 0 0
    mpt310
    October 6, 2022
    5.0 out of 5 stars Quick Read and so Helpful
    I think this is a great start to educating yourself on trauma bonds - whether you're in a toxic relationship or getting out of one. I finally build th...More
    I think this is a great start to educating yourself on trauma bonds - whether you're in a toxic relationship or getting out of one. I finally build the courage to leave my ex after 9 years and I felt like the crazy or wrong one. I started hating myself thinking "how was I so stupid?" This book is eye opening and in a sense made me feel relieved because I'm not the only one. It's not going to fix everything, but it's a really good starting place to educate yourself. I also think it's a good resource for those who know a friend/family who are in a toxic relationship to read to get a better understanding what that person might be going through.
    Helpful? 0 0
    Nunya
    July 3, 2022
    5.0 out of 5 stars Finally some answers.
    I thought I was out of my mind. I couldn’t explain to anyone what I was dealing with because I didn’t understand. This book explained most of the th...More
    I thought I was out of my mind. I couldn’t explain to anyone what I was dealing with because I didn’t understand. This book explained most of the things I dealt with and made me feel like I wasn’t crazy. I’ve be reading articles and watching clips on You Tube, instagram, and just about anything to help me. This book encapsulated all of it. It will help me move on. The unhealthy attachment is real.
    Helpful? 0 0
    Kindle Customer
    November 23, 2021
    5.0 out of 5 stars Healing the Hurt
    Great read for those who are hurting, confused, and full of why's in a Traumatic relationship. This will encourage, lift you, give you the knowledge a...More
    Great read for those who are hurting, confused, and full of why's in a Traumatic relationship. This will encourage, lift you, give you the knowledge about what and why your going through and give the tools to get out.
    Helpful? 0 0
    mrshale03
    October 14, 2021
    5.0 out of 5 stars This book changed my life
    Words can't describe how much this book has spoken to me. The way the trauma bond is described along with the personal revelations from the author com...More
    Words can't describe how much this book has spoken to me. The way the trauma bond is described along with the personal revelations from the author combine to give me understanding, acceptance and even hope. I wish I'd read this many years ago but better now than never even after 22 years of abuse.
    Helpful? 0 0
    LeAnna Banks
    October 4, 2021
    5.0 out of 5 stars Worth Reading!
    I got so much help from reading this book! I still struggle day to day but I am so glad I found this book! Thank you! Worth reading!
    Helpful? 0 0
    T11892
    July 22, 2021
    5.0 out of 5 stars Short but helpful
    Bought for my roommate and some of it was towards physical but she just used it towards emotional. She really liked it and it helped her.
    Helpful? 0 0
    chris kase
    December 8, 2020
    5.0 out of 5 stars Very Helpful
    This book has helped tremendously to validate what occurred, how I responded and that I can take responsibility for staying as long as I did, but with...More
    This book has helped tremendously to validate what occurred, how I responded and that I can take responsibility for staying as long as I did, but with explanation as to why. Easy to read.
    Helpful? 0 0
    Alyse H.
    December 4, 2020
    5.0 out of 5 stars Pure and Simple
    I thought everything going on in my situation-ship was unique...I was shocked to find it all here in this book. I’m a stickler for grammar but I did n...More
    I thought everything going on in my situation-ship was unique...I was shocked to find it all here in this book. I’m a stickler for grammar but I did not find the errors too distracting. The message and lessons in this book ring clear as a bell. The author keeps it pure and simple.
    Helpful? 0 0
    Peter
    July 24, 2020
    5.0 out of 5 stars great book
    Great reference book for people working with matrix. I have the earlier version but still buy this one because of its expanded content and low price. ...More
    Great reference book for people working with matrix. I have the earlier version but still buy this one because of its expanded content and low price. Perhaps the only minor drawback is that the printed paper is a little thin (70 gsm or lower).
    Helpful? 0 0
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