Fundamentals of Matrix Algebra by Gregory Hartman

Fundamentals of Matrix Algebra – 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.

Table of Contents

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

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About the Contributors


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

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