<p> Rutgers University-Newark Department of mathematics and Computer Science</p><p>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</p><p>TEXTBOOK: Linear Algebra with Applications (3e), Otto Bretscher Pearson/Prentice Hall Williams</p><p>This course focuses on the foundations of Linear algebra. Never hesitate to ask for extra help. Working outside class is extremely important.</p><p>We will cover the following chapters and sections:</p><p>Chapter 1 Linear Equations</p><p>Sec. 1.1 Introduction to Linear Systems Pg. 5-8 1,7,11, 15, 33, 37</p><p>Sec. 1.2 Matrices, Vectors, and Gauss-Jordan Elimination Pg. 20-24 1, 5, 19, 27, 31, 35</p><p>Sec. 1.3 0n the Solutions of Linear Systems; matrix Algebra Pg. 35-38</p><p>Chapter 2 Linear Transformations</p><p>Sec. 2.1 Introduction to Linear Transformations and Their Inverses Pg. 51-54</p><p>Sec. 2.2 Linear Transformations in geometry Pg. 66-70</p><p>Sec. 2.3 The Inverse of a Linear transformation Pg76-79</p><p>Sec. 2.4 Matrix products Pg. 89-97 Chapter 3 Subspaces of R^n and Their Dimensions</p><p>Sec. 3.1 Image and kernel of Linear transformation Pg. 109-111</p><p>Sec. 3.2 Subspaces of R^n ; Bases and Linear Independence Pg. 121-123</p><p>Sec. 3.3 The Dimension of a Subspace R^n Pg. 133-135</p><p>Sec. 3.4 Coordinates Pg. 146-149</p><p>Chapter 4 Linear Spaces</p><p>Sec. 4.1 Introduction to Linear Spaces Vector Space Rn Pg. 162-163</p><p>Sec. 4.2 Linear Transformations and Isomorphisims Pg. 169-171</p><p>Sec. 4.3 The Matrix of a Linear transformation Pg. 180-183</p><p>Chapter 5 Orthogonality and least Squares</p><p>Sec. 5.1 Orthogonal projection and Orthonormal bases Pg. 198</p><p>Sec. 5.2 Gram-Schmidt Process and QR Factorization Pg. 208</p><p>Sec. 5.3 Orthogonal Transformations and Orthogonal matrices Pg. 216</p><p>Sec. 5.5 Inner product Spaces Pg. 243</p><p>Chapter 6 Determinants</p><p>Sec. 6.1 Introduction to Determinants Pg. 259 Sec. 6.2 Properties of Determinants Pg. 271</p><p>Sec. 6.3 Geometric Interpretations of the Determinant Pg. 287</p><p>Chapter 7 Eigenvalues and Eigenvectors</p><p>Sec. 7.1 Dynamical Systems and Eigenvectors: An Introductory Example Pg. 302</p><p>Sec. 7.2 Finding the Eigenvalues of a Matrix Pg. 314</p><p>Sec. 7.3 Finding the Eigenvectors of Matrix Pg. 324</p><p>Sec. 7.4 Diagonalization Pg. 338</p><p>Sec. 7.5 Complex Eigenvalues Pg. 350</p><p>Sec. 7.6 Stability Pg. 359</p><p>Chapter 8 Symmetric matrices and Quadratic Forms</p><p>Sec. 8.1 Symmetric Matrices Pg. 370</p><p>Sec. 8.2 Quadratic Forms Pg. 378</p><p>Sec. 8.3 Singular Forms Pg. 389 </p>