Linear Algebra II is divided into seven units, listed below. The first unit provides a review of concept and techniques introduced in Mathematics 270. The remaining units deal in depth with specific, more advanced topics.

Unit 1   Review
Unit 2   General Vector Spaces
Unit 3   Vector Space Structure
Unit 4   Eigenvalues and Eigenvectors
Unit 5   Linear Transformations I
Unit 6   Linear Transformations II
Unit 7   Two Applications of Linear Algebra

Each unit includes learning objectives, which indicate what you are expected to learn from the material; indications, which tell you the order in which to do the readings and exercises; and textual material, designed to replace the instruction you would expect to receive in a regular classroom.

Work through the units carefully. Begin by reading the objectives, and keep them in mind as you proceed through the unit. Next, do the assigned readings and exercises, in the order in which they appear in the “Indications” sections. It is important that you read each section of the Study Guide or textbook three times—first for an overview, then in more detail, and finally, with pencil in hand, working out the examples and proofs.

Exercises

Two kinds of exercises are assigned in the Study Guide: mathematical problems related to material covered in the given unit and problems assigned from the textbook. Both types of exercises are designed to teach the conceptual and computational skills necessary for success in the course. Solutions to most of these exercises are given in the Study Guide or the Solutions Manual, but you should not look at them until you have made a concerted effort to solve each problem yourself.

It is important that you remember that mathematics can only be learned by doing. It is not a passive activity. Also, it is actually beneficial to be stumped at times: you are forced to think hard about a problem. When this happens, you will remember the problem and its solution more clearly.

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