Fundamentals of Matrix Algebra by Gregory Hartman
Fundamentals of Matrix Algebra - 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
What You Will Learn in Fundamentals of Matrix Algebra
"Fundamentals of Matrix Algebra" by "Gregory Hartman" is a beginner-friendly textbook that teaches "matrix algebra" with clear explanations and structured problem solving. Gregory Hartman introduces core ideas such as matrices, determinants, and vector spaces in an accessible way so students can build strong mathematical understanding. The book emphasizes both conceptual learning and practical computation.
Key topics include matrix operations, systems of linear equations, and "linear transformations". Each concept is explained step by step with examples and exercises that reinforce learning. Hartman focuses on helping students understand why mathematical methods work, not just how to use them. This approach strengthens problem-solving skills and prepares learners for advanced studies.
Overall, the textbook is ideal for students beginning linear algebra or matrix mathematics. By combining theory with practical examples, it builds a solid foundation in "mathematics" and computational thinking. Whether used in classrooms or self-study, it remains a valuable resource for understanding the fundamentals of matrix algebra and its applications.
Book Details & Specifications
Title:
Fundamentals of Matrix Algebra by Gregory Hartman
Publisher:
Virginia Military Institute
Year:
2011
Pages:
248
Type:
PDF
Language:
English
ISBN-10 #:
1467901598
ISBN-13 #:
978-1467901598
License:
CC BY-NC 3.0 US
Amazon:
Amazon
About the Author: Gregory Hartman
The author Gregory Hartman
is an Associate Professor of Mathematics at Virginia Military Institute in Lexington, Virginia. He known for teaching "matrix algebra", "linear algebra", and practical problem solving. His work focuses on simplifying mathematical concepts and helping students apply algebra in science and engineering. He emphasizes clear explanations and structured learning to build strong mathematical foundations. He authored "Fundamentals of Matrix Algebra", a textbook that introduces matrix concepts with examples and applications. The book supports learning in mathematics and computational problem solving, making it useful for students and professionals studying algebra and technical mathematics.
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