Oliver Thewalt

    Oliver Thewalt

    Theoretical Physics | Quantum Biology | Dark Matter Research | Energy Consulting | Creation of Hydrogen ATOM in the Higgs Field >> Vote for Nobel Prize

    Linear Algebra, Theory And Applications by Kenneth Kuttler

    This is a book on linear algebra and matrix theory. While it is self contained, it will work
    best for those who have already had some exposure to linear algebra. It is also assumed that
    the reader has had calculus. Some optional topics require more analysis than this, however.
    I think that the subject of linear algebra is likely the most significant topic discussed in
    undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying
    so many different topics. Linear algebra is essential in analysis, applied math, and even in
    theoretical mathematics. This is the point of view of this book, more than a presentation
    of linear algebra for its own sake. This is why there are numerous applications, some fairly
    unusual.
    This book features an ugly, elementary, and complete treatment of determinants early
    in the book. Thus it might be considered as Linear algebra done wrong. I have done this
    because of the usefulness of determinants. However, all major topics are also presented in
    an alternative manner which is independent of determinants.
    The book has an introduction to various numerical methods used in linear algebra.
    This is done because of the interesting nature of these methods. The presentation here
    emphasizes the reasons why they work. It does not discuss many important numerical
    considerations necessary to use the methods effectively. These considerations are found in
    numerical analysis texts.
    In the exercises, you may occasionally see ↑ at the beginning. This means you ought to
    have a look at the exercise above it. Some exercises develop a topic sequentially. There are
    also a few exercises which appear more than once in the book. I have done this deliberately
    because I think that these illustrate exceptionally important topics and because some people
    don’t read the whole book from start to finish but instead jump in to the middle somewhere.
    There is one on a theorem of Sylvester which appears no fewer than 3 times. Then it is also
    proved in the text. There are multiple proofs of the Cayley Hamilton theorem, some in the
    exercises. Some exercises also are included for the sake of emphasizing something which has
    been done in the preceding chapter.