By Lay, David C.
With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes 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 when they are discussed in the abstract, students are readily able to understand.
1. Linear Equations in Linear Algebra
2. Matrix Algebra
4. Vector Spaces
5. Eigenvalues and Eigenvectors
6. Orthogonality and Least Squares
7. Symmetric Matrices and Quadratic Forms
8. The Geometry of Vector Spaces
9. Optimization (Online Only)
10. Finite-State Markov Chains (Online Only)
A. Uniqueness of the Reduced Echelon Form
B. Complex Numbers