Lay D., McDonald J. Linear Algebra and Its Applications 6ed 2022

Textbook in PDF format

For courses in Linear Algebra. Fosters the concepts and skills needed for future careers.
Linear Algebra and Its Applications offers a modern elementary introduction with broad, relevant applications. With traditional texts, the early stages of the course are relatively easy as material is presented in a familiar, concrete setting, but students often hit a wall when abstract concepts are introduced. Certain concepts fundamental to the study of linear algebra (such as linear independence, vector space, and linear transformations) require time to assimilate ― and students' understanding of them is vital.
Lay, Lay, and McDonald make these concepts more accessible by introducing them early in a familiar, concrete ℝn setting, developing them gradually, and returning to them throughout the text so that students can grasp them when they are discussed in the abstract. The 6th Edition offers exciting new material, examples, and online resources, along with new topics, vignettes, and applications.
Linear Equations in Linear Algebra
Matrix Algebra
Determinants
Vector Spaces
Eigenvalues and Eigenvectors
Orthogonality and Least Squares
Symmetric Matrices and Quadratic Forms
The Geometry of Vector Spaces
Optimization
Finite-State Markov Chains
Appendixes
Uniqueness of the Reduced Echelon Form
Complex Numbers