Hunter College of The City University of New York
Hunter College of The City University of New York
MATH 260 Linear Algebra 4 hrs, 4 cr.
Textbook: Linear Algebra by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence, 4th edition, Prentice Hall, ISBN 0-13-008451-4
Chapter 1 Vector Spaces
1.1 Introduction
1.2 Vector Spaces
1.3 Subspaces
1.4 Linear Combinations and Systems of Linear Equations
1.5 Linear Dependence and Linear Independence
1.6 Bases and Dimension
Chapter 2 Transformations and Matrices
1. Linear Transformations, Null Spaces, and Ranges
2. The Matrix Representation of a Linear Transformation
3. Composition of Linear Transformations and Matrix Multiplication
4. Invertibility and Isomorphisms
5. The Change of Coordinates Matrix
Chapter 3 Elementary Matrix Operations and Systems of Linear Equations
1. Elementary Matrix Operations and Elementary Matrices
2. The Rank of a Matrix and Matrix Inverses
3. Systems of Linear Equations – Theoretical Aspects
4. Systems of Linear Equations – Computational Aspects
Index of Definitions
Chapter 4 Determinants
4. Summary – Important Facts about Determinants
Chapter 5 Diagonalization
1. Eigenvalues and Eigenvectors
2. Diagonalizability
Chapter 6 Inner Product Spaces
1. Inner Products and Norms
2. The Gram-Schmidt Orthogonalization Process
Chapter 7 Canonical Forms
1. The Jordan Canonical Form I
2. The Jordan Canonical Form II
3. The Minimal Polynomial
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