本书是一部关于线性代数的全英文教材。全书内容以线性空间和线性变换为基础展开，从而使各章内容之间内在联系紧密，给教学带来方便。

Foreword(Originally in Chinese)

Preface(for the English Translation edition)

A Note from the Translator

Explanation for the Special Notational Device

Chapter 0 Integers,Number Fields and Polynomials

Part 1 General Theory of Systems of Linear Equations Introduction

Chapter 1 Algebra of Matrices

Chapter 2 The Determinant Method for a Special Class of Lin-ear Equations(Cramer's Rule)

Chapter 3 General Theory of Systems of Linear Equations

Chapter 4 Linear Spaces and Systmes of Linear Equations

Chapter 5 Symmetric Bilinear Metric Spaces and Systems of Linear Equations

Part 2 The Principal Axes Problem of Real Quadratic Forms

Chapter 6 Linear Transformations on Linear Spaces

Chapter 7 A Class of Direct Sum Decompositions of Linear Spaces Relative to Linear Transformations

Chapter 8 Two Classes of Linear Transformations on Euclidean Spaces and the Principal Axes Problem of Quadr-atic Forms

Chapter 9 Further Development——Similarity Canonical Forms of Matrices

Bibliography

Index