Rutgers University-Newark

Rutgers University-Newark Department of mathematics and Computer Science

MATH 640:350 :02 Linear Algebra Spring 2010 Instructor : Yusuf Abdi Office: Smith Hall 314 Email Address: [email protected] Tel: (973) 353-3911 Office Hours: M,W 10:00-11:00AM

TEXTBOOK: Linear Algebra with Applications (3e), Otto Bretscher Pearson/Prentice Hall Williams

This course focuses on the foundations of Linear algebra. Never hesitate to ask for extra help. Working outside class is extremely important.

We will cover the following chapters and sections:

Chapter 1 Linear Equations

Sec. 1.1 Introduction to Linear Systems Pg. 5-8 1,7,11, 15, 33, 37

Sec. 1.2 Matrices, Vectors, and Gauss-Jordan Elimination Pg. 20-24 1, 5, 19, 27, 31, 35

Sec. 1.3 0n the Solutions of Linear Systems; matrix Algebra Pg. 35-38

Chapter 2 Linear Transformations

Sec. 2.1 Introduction to Linear Transformations and Their Inverses Pg. 51-54

Sec. 2.2 Linear Transformations in geometry Pg. 66-70

Sec. 2.3 The Inverse of a Linear transformation Pg76-79

Sec. 2.4 Matrix products Pg. 89-97 Chapter 3 Subspaces of R^n and Their Dimensions

Sec. 3.1 Image and kernel of Linear transformation Pg. 109-111

Sec. 3.2 Subspaces of R^n ; Bases and Linear Independence Pg. 121-123

Sec. 3.3 The Dimension of a Subspace R^n Pg. 133-135

Sec. 3.4 Coordinates Pg. 146-149

Chapter 4 Linear Spaces

Sec. 4.1 Introduction to Linear Spaces Vector Space Rn Pg. 162-163

Sec. 4.2 Linear Transformations and Isomorphisims Pg. 169-171

Sec. 4.3 The Matrix of a Linear transformation Pg. 180-183

Chapter 5 Orthogonality and least Squares

Sec. 5.1 Orthogonal projection and Orthonormal bases Pg. 198

Sec. 5.2 Gram-Schmidt Process and QR Factorization Pg. 208

Sec. 5.3 Orthogonal Transformations and Orthogonal matrices Pg. 216

Sec. 5.5 Inner product Spaces Pg. 243

Chapter 6 Determinants

Sec. 6.1 Introduction to Determinants Pg. 259 Sec. 6.2 Properties of Determinants Pg. 271

Sec. 6.3 Geometric Interpretations of the Determinant Pg. 287

Chapter 7 Eigenvalues and Eigenvectors

Sec. 7.1 Dynamical Systems and Eigenvectors: An Introductory Example Pg. 302

Sec. 7.2 Finding the Eigenvalues of a Matrix Pg. 314

Sec. 7.3 Finding the Eigenvectors of Matrix Pg. 324

Sec. 7.4 Diagonalization Pg. 338

Sec. 7.5 Complex Eigenvalues Pg. 350

Sec. 7.6 Stability Pg. 359

Chapter 8 Symmetric matrices and Quadratic Forms

Sec. 8.1 Symmetric Matrices Pg. 370

Sec. 8.2 Quadratic Forms Pg. 378

Sec. 8.3 Singular Forms Pg. 389