# MATH 462 Syllabus

### Linear Algebra II

Revised: September 2014

### Course Description

Topics from linear algebra including vector spaces, basis and dimension, linear transformations, orthogonality, eigenvalues, matrix similarity, diagonalization, and selected applications. Prerequisite: Math 362. Three semester hours.

### Student Learning Objectives

By the end of the course, students should be able to:

• Demonstrate understanding of the relationship between matrices, linear systems, and linear transformations;
• Explain the significance of eigenvalues and matrix decomposition in applications;
• Know, understand, and utilize definitions and statements of theorems in computations and deriving proofs;
• Demonstrate analytical skills to prove theorems and corollaries of linear algebra;
• Apply theorems to solve problems;
• Master algorithmic aspects of linear algebra; and
• Be able to present proofs and problem solutions to their peers in a clear and accurate manner.

### Text

Derek J. S. Robinson, A Course in Linear Algebra with Applications, 2nd Edition, (2006), World Scientific Publications.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

### Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

### Course Outline

• Chapter 1: Matrix Algebra (3 days)  Matrices, Operations with Matrices, and Matrices over Rings and Fields.
• Chapter 2: Systems of Linear Equations (5 days)  Gaussian Elimination, Elementary Row Operations, and Elementary Matrices with emphasis on theoretical development.
• Chapter 3: Determinants (3 days)  Permutations and Definition of Determinant, Basic Properties of Determinants, and Determinants and Inverses of Matrices with emphasis on theoretical development.
• Chapter 4: Introduction to Vector Spaces (5 days)  Vector Spaces and Subspaces, Linear Independence in Vector Spaces with emphasis on theoretical development.
• Chapter 5: Basis and Dimension (5 days)  Existence of a Basis, Row and Column Spaces of a Matrix, and Operations with Subspaces with emphasis on theoretical development.
• Chapter 6: Linear Transformations (7 days)  Functions Defined on Sets, Linear Transformations and Matrices, and Kernel, Image and Isomorphism with emphasis on theoretical development.
• Chapter 7: Orthogonality in Vector Spaces (5 days)  Scalar Products in Euclidean Space, Inner Product Spaces, Orthonormal Sets and the Gram-Schmidt Process.
• Chapter 8: Eigenvectors and Eigenvalues (3 days)  Basic Theory of Eigenvectors and Eigenvalues, Diagonalization, and Applications.
• Other topics as time allows (6 days).