Preliminaries -- Linear Transformations -- Determinants -- Row Operations -- Some Factorizations -- Spectral Theory -- Vector Spaces And Fields -- Linear Transformations -- Canonical Forms -- Markov Processes -- Inner Product Spaces -- Self Adjoint Operators -- Norms -- Numerical Methods, Eigenvalues

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. 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.

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In English.

Description based on online resource