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4434A First Course in Linear Algebra
http://www.merlot.org/merlot/viewMaterial.htm?id=297792
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. GNU Free Documentation LicenseLinear Algebra
http://www.merlot.org/merlot/viewMaterial.htm?id=302296
Linear Algebra is free for downloading, It covers the material of an undergraduate first linear algebra course.Linear Algebra, Theory and Applications
http://www.merlot.org/merlot/viewMaterial.htm?id=656501
From the preface: “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.” A solutions manual to the exercises in the textbook is included.A First Course in Linear Algebra
http://www.merlot.org/merlot/viewMaterial.htm?id=736077
'A First Course in Linear Algebra is an introductory textbook designed for university sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.״Computational and Algorithmic Linear Algebra and n-Dimensional Geometry
http://www.merlot.org/merlot/viewMaterial.htm?id=436879
״This is a sophomore level webbook on linear algebra and n-dimensional geometry with the aim of developing in college entering undergraduates skills in algorithms, computational methods, and mathematical modeling. It is written in a simple style with lots of examples so that students can read most of it on their own.״ Each chapter is downloaded separately as a pdf file. Elementary Algebra Exercise Book I
http://www.merlot.org/merlot/viewMaterial.htm?id=728508
This is a free textbook from BookBoon.'Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems in most topics in basic algebra. The problems have a wide variation in difficulty, which is indicated by the number of stars.'Elementary Linear Algebra
http://www.merlot.org/merlot/viewMaterial.htm?id=437799
״This book is an introduction to linear algebra, based on lectures given by me over 17 years, in the (now defunct) first year course MP103 at the University of Queensland. The section on subspaces is meant to be a gentle introduction to the second course, where abstract vector spaces are met in detail. Things of substance are met here, including the rank of a matrix. The section on three dimensional geometry makes use of the earlier sections on linear equations, matrices and determinants and some of the proofs are more algebraic (even pedantic) than some readers would like.״Elementary Linear Algebra
http://www.merlot.org/merlot/viewMaterial.htm?id=642706
This is a free, online textbook offered by BookBoon. "This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. This is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.״ Fundamentals of Matrix Algebra
http://www.merlot.org/merlot/viewMaterial.htm?id=427302
his text provides the reader with a solid foundation of the fundamental operations and concepts of matrix algebra. The topics include systems of linear equations, matrix arithmetic, transpose, trace, determinant, eigenvalues/vectors, and linear transformations, focusing largely on transformations of the Cartesian plane.The text is designed to be easily read, written in a casual style. Key concepts are explained, but rigorous proofs are omitted. Numerous examples are provided to illuminate new ideas and provide practice. Each section ends with exercises (with answers to odd questions appearing in the back).The text is currently in use by Cadets of the Virginia Military Institute. It is appropriate for undergraduates in mathematics and the sciences, as well as advanced high school students.Geometry Unbound
http://www.merlot.org/merlot/viewMaterial.htm?id=906160
'This book is not written in the manner of a typical textbook. (Indeed, it is not really designed to serve as a textbook at all, though it could certainly be used as one with highly motivated students.) That is, we do not present full developments of key theorems up front, leaving only routine exercises for the reader to consider. For one, we leave strategic gaps in the exposition for the reader to fill in. For another, we include a number of nonroutine problems, of the sort found on the IMO or related national competitions. The reader may or may not succeed in solving these, but attempting them should provide a solid test of one’s understanding. In any case, solutions to the exercises and problems are included in the back; we have kept these brief, and they are only intended to make sense once you have already thought a bit about the corresponding exercises/problems on your own.''Aside from this introduction, the book is divided into four parts. The first part, “Rudiments”, is devoted to the foundations of Euclidean geometry and to some of the most pervasive ideas within the subject. The second part, “Special situations”, treats some common environments of classical synthetic geometry; it is here where one encounters many of the challenging Olympiad problems which helped inspire this book. The third part, “The roads to modern geometry”, consists of two4 chapters which treat slightly more advanced topics (inversive and projective geometry). The fourth part, “Odds and ends”, is the back matter of the book, to be consulted as the need arises; it includes hints for the exercises and problems (for more on the difference, see below), plus bibliographic references, suggestions for further reading, information about the open source license, and an index.'