Preface for the Instructor xv
Section Prerequisite
Section 8.8 (Computer Graphics) Section 5.2 (The Matrix of a Linear Transformation)
Section 8.9 (Differential Equations)** Section 5.6 (Diagonalization of Linear Operators)
Section 8.10 (Least-Squares Section 6.2 (Orthogonal Complements)
Solutions for Inconsistent Systems)
Section 8.11 (Quadratic Forms) Section 6.3 (Orthogonal Diagonalization)
Section 9.1 (Numerical Methods for Section 2.3 (Equivalent Systems, Rank,
Solving Systems) and Row Space)
Section 9.2 (LDU Decomposition) Section 2.4 (Inverses of Matrices)
Section 9.3 (The Power Method Section 3.4 (Eigenvalues and Diagonalization)
for Finding Eigenvalues)
Section 9.4 (QR Factorization) Section 6.1 (Orthogonal Bases and the Gram-Schmidt
Process)
Section 9.5 (Singular Value Section 6.3 (Orthogonal Diagonalization)
Decomposition)
(Continued)
*In addition to the prerequisites listed, each section in Chapter 7 requires the sections of Chapter 7 that precede
it, although most of Section 7.5 can be covered without having covered Sections 7.1 through 7.4 by concentrating
only on real inner products.
**The techniques presented for solving differential equations in Section 8.9 require only Section 3.4 as a
prerequisite. However, terminology from Chapters 4 and 5 is used throughout Section 8.9.
PLANS FOR COVERAGE
Chapters 1 through 6 have been written in a sequential fashion. Each section is gen-
erally needed as a prerequisite for what follows.Therefore, we recommend that these
sections be covered in order. However, there are three exceptions:
■ Section 1.3 (An Introduction to Proofs) can be covered,in whole, or in part,
at any time after Section 1.2.
■ Section 3.3 (Further Properties of the Determinant) contains some material
that can be omitted without affecting most of the remaining development. The
topics of general cofactor expansion,(classical) adjoint matrix,and Cramer’s Rule
are used very sparingly in the rest of the text.
■ Section 6.1 (Orthogonal Bases and the Gram-Schmidt Process) can be
covered any time after Chapter 4, as can much of the material in Section 6.2
(Orthogonal Complements).
Any section in Chapters 7 through 9 can be covered at any time as long as the
prerequisites for that section have previously been covered. (Consult the Prerequisite
Chart for Sections in Chapters 7, 8, 9.)
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