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 Procedure
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).