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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