This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.
All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.
Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text.
Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.

First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.

A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This third edition corrects several errors in the text and updates the font faces.

These notes are intended to provide a brief, noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.

We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book.

Linear Algebra is a text for a first US undergraduate Linear Algebra course. It is Free. You can use it as a main text, as a supplement, or for independent study.

This 10-minute video lesson looks at Determinants: Finding the determinant of a 3x3 matrix.

This 22-minute video lesson shows another example of a projection matrix. It shows how to figure out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.

This 15-minute video lesson sees that orthonormal bases make for good coordinate systems.

This 3-minute video lesson is a correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant.

The Linear Algebra course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in November 2018. The course is part of the Ohio Transfer Module and is also named OMT019. For more information about credit transfer between Ohio colleges and universities, please visit: transfercredit.ohio.govTeam LeadAnna Davis                                         Ohio Dominican UniversityContent ContributorsPaul Bender                                       Ohio Dominican UniversityRosemarie Emanuele                        Ursuline CollegePaul Zachlin                                       Lakeland Community CollegeLibrarianDaniel Dotson                                    Ohio State University                     Review TeamJim Fowler                                         Ohio State UniversityJim Cottrill                                          Ohio Dominican University

This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.

This 25-minute video lesson introduces the idea of an angle between two vectors.

This 10-minute video lesson looks at what happens to the determinant when we perform a row operation.

This 13-minute video lesson looks at the determinant when a row is multiplied by a scalar.

This 17-minute video lesson looks at the determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices).

This 22-minute video lesson realizes that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix.

This 20-minute video lesson shows how to view the determinant of the transformation matrix as a scaling factor of regions.

This 14-minute video lesson shows the proof by induction that transposing a matrix does not change its determinant.

This 9-minute video lesson shows how to find the determinant by going along other rows or columns.