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Fundamentals of Matrix Algebra

(1 review)

Gregory Hartman, Virginia Military Institute

Pub Date: 2011

Publisher: APEX Calculus

Language: English

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CC BY-NC

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Reviewed by Tim Brauch, Associate Professor, Manchester University on 6/15/19

The author makes clear in the foreword that this text is not a linear algebra text. It avoids much of the theory associated with linear algebra; although, the author does touch on theorems as necessary. Avoiding theory but using the term... read more

 

Table of Contents

1 Systems of Linear Equations

  • 1.1 Introduction to Linear Equations
  • 1.2 Using Matrices To Solve Systems of Linear Equations
  • 1.3 Elementary Row Operations and Gaussian Elimination
  • 1.4 Existence and Uniqueness of Solutions
  • 1.5 Applications of Linear Systems

2 Matrix Arithmetic

  • 2.1 Matrix Addition and Scalar Multiplication
  • 2.2 Matrix Multiplication
  • 2.3 Visualizing Matrix Arithmetic in 2D
  • 2.4 Vector Solutions to Linear Systems
  • 2.5 Solving Matrix Equations AX = B
  • 2.6 The Matrix Inverse
  • 2.7 Properties of the Matrix Inverse

3 Operations on Matrices

  • 3.1 The Matrix Transpose
  • 3.2 The Matrix Trace
  • 3.3 The Determinant
  • 3.4 Properties of the Determinant
  • 3.5 Cramer’s Rule

4 Eigenvalues and Eigenvectors

  • 4.1 Eigenvalues and Eigenvectors
  • 4.2 Properties of Eigenvalues and Eigenvectors

5 Graphical Explorations of Vectors

  • 5.1 Transformations of the Cartesian Plane
  • 5.2 Properties of Linear Transformations
  • 5.3 Visualizing Vectors: Vectors in Three Dimensions

About the Book

A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This third edition corrects several errors in the text and updates the font faces.

About the Contributors

Author

Gregory Hartman, Ph.D., Department Applied Mathematics, Virginia Military Institute