Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick 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. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible. Features are Fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, and then gradually examined from different points of view. Later generalizations of these concepts appear as natural extensions of familiar ideas. Focus on visualization of concepts throughout the book helps readers grasp the concepts. Icons in the margins to flag topics for which expanded or enhanced material is available on the textbook’s companion Website..
A modern view of matrix multiplication is presented, with definitions and proofs focusing on the columns of a matrix rather than on the matrix entries.
Numerical Notes give a realistic flavor to the text. Students are reminded frequently of issues that arise in the real-life use of linear algebra. Each major concept in the course is given a geometric interpretation because many students learn better when they can visualize an idea. [M] exercises appear in every section. To be solved with the aid of a [M]atrix program such as MATLAB™, Maple®, Mathematica®, MathCad®, Derive® or programmable calculators with matrix capabilities, such as the TI-83 Plus®, TI-86®, TI-89®, and HP-48G®. Data for these exercises are provided on the Web