Between 2002-2007, the Introduction to Matrix Algebra book was downloaded free of charge by more than 30,000 users from 50 different countries. This book is an extended primer for undergraduate... More > Matrix Algebra. The book is either to be used as a refresher material for students who have already taken a course in Matrix Algebra or used as a just-in-time tool if the burden of teaching Matrix Algebra has been placed on several courses. In my own department, the Linear Algebra course was taken out of the curriculum a decade ago. It is now taught just in time in courses like Statics, Programming Concepts, Vibrations, and Controls.
There are ten chapters in the book 1) INTRODUCTION, 2) VECTORS, 3) BINARY MATRIX OPERATIONS, 4) UNARY MATRIX OPERATIONS, 5) SYSTEM OF EQUATIONS, 6) GAUSSIAN ELIMINATION, 7) LU DECOMPOSITION, 8) GAUSS-SEIDAL METHOD, 9) ADEQUACY OF SOLUTIONS, 10) EIGENVALUES AND EIGENVECTORS.< Less

This 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,... More > 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, and is appropriate for undergraduates in mathematics and the sciences, as well as advanced high school students.< Less

This 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,... More > 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, and is appropriate for undergraduates in mathematics and the sciences, as well as advanced high school students.< Less

The use of choice examples to show the practical application of matrix algebra and related mathematical tools in specific problems, it serves also as an introduction to linear programming, fluid... More > mechanics, vector analysis and rf cicuit design.The full workings and code are made available for the use and adaptation of the reader.
Here we walk through examples of using linear algebra and matrices to solve problems like cost estimation, we show how similar techniques are used in electrical theory and circuit design. We show how ballistics can predict the range of a football and the time of travel of a bullet. We see how we can generate 3d transforms of rotation and reflection
of objects about general axes and mirrors. We look at the problem of signal rejection in transmission lines and give worked solutions.< Less

The Formal Linear Algebra Methods Environment (FLAME) encompasses a
methodology for deriving an algorithm for a dense linear
algebra operation hand-in-hand with its proof of correctness
as well as... More > an approach to represent (and code) the
resulting algorithm. This books reviews the foundations of FLAME:
the derivation methodology, the notation, and the high-level Application
Programming Interfaces, which are applied to basic linear algebra operations as well as operations for the solution of linear systems.
While the text targets the novice, its emphasis on high performance
algorithms should also be of interest to the expert.< Less

The Formal Linear Algebra Methods Environment (FLAME) encompasses a
methodology for deriving an algorithm for a dense linear
algebra operation hand-in-hand with its proof of correctness
as well as... More > an approach to represent (and code) the
resulting algorithm. This books reviews the foundations of FLAME:
the derivation methodology, the notation, and the high-level Application
Programming Interfaces, which are applied to basic linear algebra operations as well as operations for the solution of linear systems.
While the text targets the novice, its emphasis on high performance
algorithms should also be of interest to the expert.< Less

Linear Algebra by Jim Hefferon is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Hardcover copies are available for the cost of manufacturing (the... More > publisher receives no additional revenue). The book covers the material of a first undergraduate Linear Algebra course. The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: a semester of calculus. Students with three semesters of calculus can skip a few sections. The approach is developmental. It does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.< Less

Linear Algebra by Jim Hefferon is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Hardcover copies are available for the cost of manufacturing (the... More > publisher receives no additional revenue). The book covers the material of a first undergraduate Linear Algebra course. The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: a semester of calculus. Students with three semesters of calculus can skip a few sections. The approach is developmental. It does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.< Less

This book covers college algebra. The topics include the following:
Polynomial, Nonlinear, and Radical Equations; Sets, Relations, Functions; Absolute Value Equations and Inequalities; Linear... More > Programming; Graphs of Functions; Asymptotes; Logarithms; Exponential and Logarithmic Equations; Graphs of Exponential and Logarithmic Functions; Matrix and Matrix Methods; Determinants; Complex Numbers and Operations; Polar Form of Complex Numbers; Roots of Complex Numbers; Graphing Polar Coordinates and Equations; Conic sections;; Remainder and Factor Theorems; Rational Roots; Partial Fractions; Sequences and Series; Binomial Theorem; Permutations and Combinations; and Mathematical Induction;< Less

This book covers both algebra and trigonometry. The topics include the following: Polynomial, Nonlinear, and Radical Equations; Sets, Relations, Functions; Absolute Value Equations and Inequalities;... More > Linear Programming; Graphs of Functions; Asymptotes; Logarithms; Exponential and Logarithmic Equations; Graphs of Exponential and Logarithmic Functions; Matrix and Matrix Methods; Determinants; Complex Numbers and Operations; Polar Form of Complex Numbers; Roots of Complex Numbers; Graphing Polar Coordinates and Equations; Conic sections;; Remainder and Factor Theorems; Rational Roots; Partial Fractions; Sequences and Series; Binomial Theorem; Permutations and Combinations; Mathematical Induction; Right Triangle Trigonometry; Trigonometry of Real Numbers; Graphs of Trigonometric Functions; Graphs of Inverse Trigonometric Functions; Trigonometric identities and Equations.< Less